By the 1950s the US could make bombs as big as it wanted. It fielded a weapon with a yield of 25 megatons in the early 1960s and never made anything bigger.

The problem is, when you increase the explosive power of a weapon, you end up increasing the weight. The relationship between weapon weight and yield is roughly linear. You get some increasing efficiency the more fusion you use in the weapon, but there are limits because of all of apparatus is takes to start the reactions.

OK, so what? Well the blast damage of a weapon is not linear with yield. It goes up as a cubic root. This is because you are essentially increasing the volume of a "sphere" of blast — and the surface area is not going to go up proportionally with the volume. So the rule of thumb is that to multiply the blast damage of a weapon by 2, you have to multiply the yield by 8.

So there are severe diminishing returns, in terms of the amount of increased damage versus the amount of increased weight. The only place where this isn't quite as bad a trade-off is in terms of thermal damage, which goes up a bit better than blast, but it turns out that the number of applications where you need huge areas of thermal radiation are pretty few and far between. (They looked into this as a way of maybe blowing other nukes out of the sky, but it's not a very effective way to try and target structures on the ground.)

So in practice, two 5 megaton weapons will weigh about the same as a single 10 megaton weapon, but if you space them well, can do more damage than the 10 megaton weapon. So instead of trying to make bigger and bigger bombs, you try to find bombs that are in a "sweet spot" of what your delivery vehicles can carry.

What they ended up focusing on were weapons of fairly good yield-to-weight ratios that could be fit into a volume about the size of a trash can. These are very tricked out, very sophisticated hydrogen bombs — much more sophisticated than the high-yield weapons, which are just the scaling up of existing ideas. These new warheads had yields that ranged from around 100 kt up to about 500 kt, but could be fit into such small sizes that you could put 10 of them on a single missile (MIRVing). Couple that with increased accuracy of the warheads, and you can drop an impressive amount of blast pressure pretty much anywhere you want, and do it in a way that can't be shot down. That's more than you can say for any bomber trying to haul a weapon with the aerodynamic characteristics of a school bus, as weapons in the tens of megatons tend to be.

As an aside, after the Soviets detonated a 50 Mt weapon that could be scaled up to 100 Mt in 1961, the USA did consider making 100 Mt weapons, and even got some quotes from the various weapons labs about what that would entail. For awhile the AEC and DOD were bullish on the idea, but Kennedy wasn't too convinced. The signing of the Limited Test Ban Treaty essentially ended those efforts, which were mostly on paper up to that point anyway. This was actually an open discussion in Congress at the time, the fact that the LTBT would limit US work on weapons of such high yield. It was a trade-off the US was willing to make, in the end, because they didn't foresee a lot of need for "very high yield" weapons in their future — their utility was very limited.

Robert McNamara put it this way when testifying before Congress in 1963 about the LTBT's impact on the US future stockpile:

But the question is, and has been for some time: Is there a military advantage to the United States in deployment of very high yield weapons? For some years we have examined this question.

One possible use of the very high-yield weapons would be to deliver them by missile and detonated them at altitudes of 100,000 feet and above, presumably over cities. Detonation at such altitudes could cause significant thermal damage — fire, or fire storms, and this is over hundreds of square miles. But a better way to achieve even greater destruction, and a way which is within the present U.S. capabilities, is to divide the attack among several smaller weapons so as to saturate any ballistic missile defenses.

Another potential mission for the very high-yield weapons might be to use them to strike very hard underground targets. As for this mission, the judgment is that, except for command posts placed thousands of feed deep in rock, the objective can be achieved at least as well by the expenditure of larger numbers of smaller weapons. In any case, it seems agreed that command posts can be constructed at sufficiently great depths to preclude their destruction even by surface detonation of 100 megaton bombs. ...

As a result of our consideration of these very high-yield weapons, we have concluded that there are two military disadvantages to deploying them as contrasted with deploying a larger number of smaller weapons.

First, as I have said, our studies indicate that for most missions directed at military targets, we can achieve a higher confidence of kill by using two or three smaller weapons instead of one very large on; for a given resource input we achieve higher target destruction with our smaller systems.

Second, very high-yield warheads are relatively inferior as second strike, retaliation, weapons; it is much more difficult and costly to make them survivable — to harden, camouflage or make mobile the huge missiles required to deliver these weapons.

There is more, but you get the drift. I want to emphasize that the US scientists and even policymakers did, at times, make studies of weapons in the 50-100 megaton range, and even weapons in the range of 1,000 or 10,000 megatons. Eisenhower himself personally vetoed a 60 megaton proposal, claiming the warheads were "already too big," but these questions persisted through the Johnson administration at least. In the end, the military itself concluded that it didn't really need weapons of these sizes — it could make do with the massive arsenals it already had. Keep in mind that by the mid-1970s, each Ohio class submarine carried 24 Trident I missiles, each missile loaded with eight 100 kt warheads. The missiles had ranges of some 7,400 km and a CEP of 450 m (which means you had a 93% chance of putting it within 900 m of a target — pretty dang accurate). So each sub is carrying 19.2 Mt, but parceled into 192 separate targets. We had eight subs in the fleet, so that's 154 Mt or so, parceled into 1,536 targets, just from this one fleet of subs. You can see how much more interesting such a thing would be for a military planner, rather than investing the effort into putting 100 Mt in one big, heavy bomb.

I have written a bit about this here. I also have a interactive visualization of the US nuclear stockpile that allows you to visualize the historical trends in weapons yields and weighs. This yield-to-weight ratio is how weapons designers talk about sophistication, not raw explosive yield. I am at present doing research into US work on "very high yield" nuclear weapons — there was always some interest, but these other trends prevailed. It is less that politics precluded very large weapons, it is more that highly-deliverable weapons with good yield-to-weight ratios offered up many more strategic possibilities. If you have a lot of accurate 500 kt bombs, you're never going to lack for sheer destructive power, if that's what you're going for, but you also have the option to do things other than take out entire metro areas, which is mostly what weapons in the +15 megaton range are all that good for.

They're not useful.

Bombs explode in 3 dimensions, but cities are mostly two dimensional. Multi-megaton weapons were deployed in an era where delivery systems had an accuracy on the order of a kilometer or several. If you miss a target by 3km but use a multi-megaton warhead you'll still take out the target.

In the late 60s missile technology advanced in two important ways. First by vastly increasing the precision targeting of warheads (down to a few hundred meters). Second by the development of multiple independently targeted reentry vehicles (MIRV) technology. This meant you could replace a single 3 or 10 MT warhead with many sub-megaton miniaturized warheads on a single missile. Which could blanket a large population center or take out multiple point targets.

This is a much more effective and efficient use of missiles and of nuclear weapons material (plutonium, uranium, fusion fuel, etc.)

Interestingly, MIRVing and miniaturization were so incredibly effective that they kicked off an arms race. The advent of ICBMs and thermonuclear weapons had already ushered in an arms race between the US and Soviets but MIRVing kicked it into high gear. There are several reasons for this. The use of MIRVing and advanced high-efficiency warheads means that you get a lot more bang for your buck and you can do a lot more damage and take out a lot more targets with a single missile.

Moreover, MIRVes are harder to take out with anti-ballistic missile (ABM) systems. Remember that big thermonuclear weapons are a "horseshoes and handgrenades" style weapon, you just need to get within a few km to take out the target. This also works when taking out a warhead with another warheads. If you can steer a missile within a few km of another warhead you can then use a few megaton bomb to destroy that warhead exoatmospherically or even during the reentry phase. Exploding a 3MT bomb at, say, 50km altitude wouldn't be ideal, but the people on the ground wouldn't even have 3rd degree burns, and it would be vastly preferable to letting a 10MT bomb explode near the surface. ABMs are very effective against single warheads, since it's a 1 for 1 tradeoff, and also the ABM doesn't need to have the same range as an ICBM. But MIRVed warheads change that balance dramatically. It's very likely that even a very large ABM warhead would only be able to take out one or maybe two or three MIRV warheads due to their being spread out with a separation of several km. Also, MIRVing makes it vastly easier to use "penetration aids" with every missile. These can be things ranging from chaff (to screw up radar systems), radar jammers, or decoys (inflated mylar balloons that mimic the radar signature of a warhead). With the technology of the 1960s it was nearly impossible to distinguish between a decoy warhead and the real thing, and there could easily be many more decoys than real warheads, so the chances of even a very robust ABM arsenal taking out a significant fraction of incoming warheads was low.

The advent of ABM systems further escalated the runaway arms race that had already kicked into high gear due to the advent of ICBMs, and MIRVed miniaturized thermonuclear weapons. Between 1955 and 1965 the number of deployed warheads in the world increased by a factor of 10, with much more than a factor of 10 increase in destructive capability. As each side pursued ABM systems it drove the other side to improve their missiles, MIRV systems, warheads, and penetration aid systems that much more to ensure "survivability" of the warheads in a nuclear strike.

It didn't take long for both sides to realize the arms race was unsustainable and reckless, which led to the Strategic Arms Limitation Talks (SALT) and the ABM and SALT I treaties taking effect in the early 1970s. These treaties limited "strategic" warhead deployments as well as ABM installations (countries were allowed a limited number of ABM sites, the Soviets retained theirs around Moscow but the US dismantled all of its ABM sites).

MIRV technology continued to advance but deployments did not escalate. Though it's worth considering what the most extreme case could have been if the arms race hadn't ended. Consider the Ohio-class submarine, the Trident D5 missile, and the W88 warhead. There were 24 Ohio-class submarines planned, each of which could carry up to 288 W-88 warheads with 475 kt warheads. With nearly 7000 warheads, more than 3 gigatons of explosive yield, it would have been possible to completely devastate 1.6 million square kilometers of land, or nearly 1/5th of the continental US. That's enough to take out nearly all cities on Earth, and 3+ billion people, just with 2 dozen nuclear submarines, not even factoring in land-based weapons or other nations' arsenals. In a full-scale exchange at the culmination of an unrestrained nuclear arms race the devastation would be unimaginable.

Edit: fixed a typo.