One needs to understand the sizes of the various nuclear arsenals as the result of historical forces and national pressures (both domestic and international). None came out of nowhere.

In the late 1940s through the early 1960s, the US arsenal swelled to almost unfathomable size. In the 1950s the was adding thousands of new warheads to its arsenal per year. This was the result of a massive push — essentially the Atomic Energy Commission was asked to produce as many warheads as it could contemplate doing, because the military claimed it needed all of them. These were the years of what was known as "nuclear plenty": the US had upgraded its fissile material production system in the late 1940s and was rapidly innovating in both warhead design and delivery vehicles. It felt it was in a race with the USSR (somewhat correctly, though it often underestimated how vastly ahead of the Soviets it was in this race), and that the only way to guarantee security was with a massive stockpile. What factors lead to the idea that a stockpile in the tens of thousands was required? Several: 1. a desire for almost total confidence in the destruction of the USSR, which meant redundant targeting to compensate for bomber defenses, missile failures, a Soviet sneak attack, etc., 2. interservice rivalries meant the USAF, Army, and USN each pursued their own independent and often uncoordinated stockpiles, 3. pessimistic target models assumed they would need more (and larger) weapons than they probably did require to knock out key targets, 4. the push for tactical nuclear weapons in the late 1950s drove much of those gains (in the late 1950s-1960s, at times much more than half of the stockpile was tactical, not strategic) and 5. the entire program and deliberation was swathed in extreme secrecy that prevented deliberation and reconsideration of other options.

By the end of the 1960s, several reforms to the planning process (e.g. the creation of the SIOP process), along with efforts at arms control, as well as a realization that a bloated stockpile was not necessarily an advantage (and came with steep fiscal costs), led to the decline in such massive additions, but the stockpile stayed at over 20,000 warheads until the end of the Cold War. Total deployed warheads actually increased, however, as MIRVed systems allowed more warheads to be placed per delivery vehicle; US peak deployed was around 14,000 strategic warheads in the mid-1980s, and Soviet peak deployed was around 12,000 slightly later. (The differences between total warheads and force loadings — notably the warheads deployed — is often overlooked when looking at simple warhead counting charts. It's not how many warheads you have that matters, in the end; it's how many you are ready to deliver. It is also important to note that the technology of warheads and their delivery vehicles has change over time, generally leading to smaller-yield warheads and more accurate vehicles after the boom of the 1950s-60s. See my Yield-to-weight explorer to look at the data visualization of how warhead types changed over time in the USA.)

The Soviets mirrored much of this logic and practice, but with even more secrecy and even more of a feeling of needing to "catch up." The Soviet arsenal continued rising at a steep rate until the late 1980s, when its own fiscal problems caught up with it, and arms control possibilities seemed to offer a better way towards safety.

In the post-Cold War, both of the superpowers ended up, through the work of treaties like SALT and START, reducing their nuclear forces considerably, both for the goals of increased safety and stability, but also with an eye towards long-term maintainability and fiscal accounting. These reductions have led both sides to end up with around 2,000 warheads deployed — considerably less than their Cold War peaks. As for why so many today, one finds nebulous answers. If you ask US planning officials, they will tell you that they need these many weapons because the Russians have that many weapons; they only will consider reducing them as a diplomatic tit-for-tat. (In fact, at times they have argued that even obsolete or unnecessary systems should be kept, just so we could feel good negotiating them away.) They also argue that most warheads are targeting other warheads, so if you remove one system, the enemy will simply re-target their warheads at other targets (the "warhead sponge" argument, which imagines the Russians do not have similar financial issues as we do, and would not leap at the opportunity to decrease their own deployments). And there is the ever-present confidence issue: if you think your warheads have an X% chance of missing your targets, then you need to target more warheads. The US targeting culture in particular does not like uncertainty and so errs on the side of overkill, typically. (The Russians seem more accepting of uncertainty, on the whole.)

What of the others? The arsenals of the UK and France were both meant to augment the US deterrence, in a sense, by showing the Soviets that the US was not the only power to take into consideration, and to push aside any thoughts that maybe the US would sacrifice Europe if it got to keep its own citizens alive. These arsenals were never meant to be able to totally repel or destroy the USSR: they were meant to increase the costs of war with NATO and Western Europe, and to give these countries (the UK and France) a bigger "seat at the table" in discussing the security of Europe. Neither the UK nor France were interested in spending a superpower's wages to grow their arsenals; both had more fiscally reduced programs than the US and USSR.

The People's Republic of China deliberately did not grow their arsenal as fast as they possibly could have, and deliberately stopped it at a relatively modest number (around 300). The PRC policy on nuclear weapons, since the 1960s, has been to emphasize that the PRC was never aiming to be able to actively threaten the US or USSR with a full-scale attack; they were purely retaliatory, a "second-strike" force posture that complemented their stated "no first use" policy. So in this case, keeping their arsenal relatively limited was meant to be a security measure: clearly indicating to the US and USSR that they had no intention of striking first (they could not hope to destroy either states' weapons entirely with such a small force), but that the consequences of launching on the PRC could be dire.

India and Pakistan have increased their arsenals at about the maximum rate they have found it possible. They are the only countries seeking to actively increase their stockpiles as fast as they can produce new warheads, as far as we can tell. They are limited by their production facilities, which are relatively modest compared to the Cold War ones. They are locked in a mirroring dynamic, neither interested in letting the other country "pull ahead," neither actively involved in discussions about freezing their arsenal sizes.

This is hardly a comprehensive answer, and there are many devils in the details. But I hope it sketches a bit of a useful overview for thinking about these stockpile histories. It is not as easy as saying "the US and USSR are larger," though the fact that they had more resources to spend, and were willing to spend them, is part of the story.

It stems from the fact that other nuclear powers were comparatively late to the party and didn't have the industrial and economic capacity to support a massive arsenal nor the kind of strategic goals that the US and USSR had that required such a massive arsenal.

First, let's look at the reasoning behind the sizes of the American and Soviet nuclear arsenals. Soviet and American strategy was largely built around the idea of massive nuclear exchanges at the other's strategic targets, which included command and control centers, conventional forces, industrial targets, and, most importantly of all, the other guy's warheads. In a nuclear exchange, the idea was that your side would be able to destroy enough of the other side's weapons before they could be deployed, ultimately leaving a situation where one side has lost its capacity to respond to a nuclear attack in kind. From a defensive perspective, the ideal defense becomes arranging your targets in such a way that the other guy can't deploy his warheads in an efficient manner - e.g. hardening targets to require direct hits by very large weapons, spreading silos about so that every silo requires its own warhead, having 24/7 patrols of bombers so they can't be caught on the ground, etc. Obviously, the response to this becomes simply building more warheads. This resiliency doesn't really protect whatever is hit, but it makes it significantly more likely that friendly warheads will survive an initial surprise attack and allow significant enough retaliation so as to deter that attack from happening in the first place. Ultimately, it boils down to a capabilities race, because one side having too much of an edge in warheads creates a situation where one side now has the ability to fully neutralize the other's strategic arsenal while the other can't.

America and the USSR, being the two largest industrial powers in the world and the first two nuclear powers, obviously had a head start on things. They were both able to support massive strategic weapons programs, and tensions between them ensured that an arms race would kick off relatively quickly.

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For the other nuclear powers, however, they lacked both the industrial capacity and time-lead to have any chance of reaching this kind of strategic parity with the US or Soviets. Thus, nuclear weapons became more of a one-sided deterrent with a heavy focus on tactical strikes and retaliatory strike capabilities. The British were a prime example of this. The V-bombers were designed from the ground up to not provide any kind of parity with the Soviets, but rather to provide a nuclear delivery device capable of hitting cities in the Soviet Union to give the British a credible means of retaliation in the event of a nuclear strike. As air defenses improved and the shift to low-altitude bombing made the V-bombers obsolete, the British shifted to ballistic missile submarines as their sole delivery means, which traditionally have offered any operator a resilient means to launch a retaliatory strike. The French were similar - per original specifications for the Dassault Mirage IV, the French hoped to have a strike aircraft that could just barely reach cities in the Soviet Union. Unlike Britain, they retain air-launched nuclear strike capabilities in the form of to this day, but they also shifted the bulk of their deterrent to ballistic missile submarines. We see similar thinking with other nuclear powers as well. The Swedes were developing nuclear weapons in hopes of making a Soviet invasion too costly to be worth it, and the rationale for the alleged Israeli nuclear arsenal is similar with respect to hostile Arab neighbors. South Africa had slightly different motives - their deterrent was aimed more locally, as the Soviets and Cubans were actively sponsoring rebel groups and neighboring governments hostile to South Africa as they became increasingly isolated among the international community.

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India and Pakistan are the only real outliers - their arsenals are very clearly aimed at each other, and while they nominally have the same kind of deterrent strategy as every other minor nuclear power (as a retaliatory measure to make invasion not worth it), their relative parity means they have the potential for the kind of arms race we had between the US and Soviets.