During the 40's tanks evolved incredibly fast, gaining huge amounts of armor and guns becoming more than twice as large, but then kinda stopped. What happened after the war when it comes to tank development?
I'd argue quite the opposite, in fact- a lot of the development you see during the war has to do with changes in doctrine and employment of tanks, with the base technology remaining much the same, while development in the post-war period is where you see real advancements in the technology (though doctrine was still evolving as well).
Before the war and in its early stages, tank designs split into two categories- slower, heavier 'infantry' tanks that were designed to support the infantry at the front lines, and faster, lighter 'cruiser' or 'cavalry' tanks that were intended to exploit a break in the lines and then operate in the enemy's strategic depth, fouling supply lines and communication. Neither were intended to combat enemy tanks- that role was reserved for tank destroyers, which were armed with long-range, larger-caliber guns, but less suited for mobile combat- most German designs had no turret, mounting the gun in a casemate, while American destroyers generally had open turrets, neither of which is something you want in an offensive role. One of the most interesting outcomes of this split-level doctrine is that, in the early stages of the war, the Germans fielded a tank (the Panzer I) that actually had no cannon at all, only dual machine guns, and weighed less than 6 tonnes (less than 2 Hummers, for comparison). These designs would not last very long.
When war broke out, the capabilities of the new generation of armored vehicles surprised both sides. As the saying goes, generals perfect the art of fighting the last war just in time for the next one, and so the swift, decisive war of maneuver that occurred came as a shock to commanders expecting WWI redux, and forced a reassessment of tank design and employment. The need that became increasingly clear was for a sort of combination tank- one that was heavily armored like an infantry tank, could strike quickly and decisively like a cruiser tank, and had armament like a tank destroyer in order to engage enemy tanks. This concept led to the most widely produced and successful tanks of the war- the M4 Sherman, Panzer IV, and T-34. These were remarkably similar designs, weighing in the range of 25-30 tonnes, and armed with a ~75mm rifled main gun with 2 or 3 supporting machine guns, and they dominate what we think of when WWII tank combat. There were, of course, still light tanks, tank destroyers, and heavy tanks (which I'll get to next), but these medium tanks were central to intrawar tank employment.
Right now, you may be thinking, "But what about the Tiger?" As you mentioned, tanks tended to get bigger and heavier as the war went on, and the Tiger I and II represent the pinnacle of this, being the largest and heaviest tanks employed in any significant numbers. They were rightly feared, and did massive amounts of damage when effectively employed, but they had a number of drawbacks. Because of their size (about 70 tonnes), simply moving them around was difficult. They had worse performance than lighter tanks in poor ground conditions, tending to damage dirt roads and not do well in mud. They couldn't use many bridges (especially temporary or jury-rigged ones) that lighter tanks were able to handle. They tended to break down quite a bit, and their size played more of a role in this then you'd think- for one, that weight was essentially at the upper limit of what the suspension system employed could handle. Because of all these issues, the Tiger line of tanks represent a high-water mark in tank design, at least in terms of size. The closest modern tank to it in size is the M1 Abrams, at 60 tonnes, and even that is quite a bit more mass than many other designs.
Now, what happened after the war is where things get interesting. The only real technological breakthrough during the war (though it was a big one) were HEAT rounds, which use a shaped charge to penetrate armor. All tanks used solid steel armor, fired from rifled guns using stadiametric sights, etc., etc. During the Cold War, however, you see a massive boom in development. Composite armor (using ceramics, elastic materials, etc., in addition to steel) vastly improved armor performance for a given weight. Other armor improvements include explosive reactive armor and wire cages to cause HEAT rounds to detonate early.Guns mostly switched over to smoothbore, the better to fire new, more advanced HEAT-type rounds, and also for kinetic energy penetrators (also known as sabot rounds). Sighting technology and corresponding countermeasures made massive leaps- infrared sighting, computer-adjusted sighting, wind and barrel wear adjustments, laser rangefinding, and then infrared camouflage, laser detection systems and countermeasures. Wire-guided missiles and other new types of armament came into play, as did the necessary technology to defeat them, including hard-kill computer-controlled systems. All of this combined puts modern battle tanks light-years ahead of any WWII design- a M4 firing a 1940s tank round would hardly chip the paint on an Abrams or T-90, and it wouldn't get the chance to try, because it would have been destroyed before it even knew the enemy was there.
Sources: "The Rommel Papers", by B.H. Liddell Hart (available online: https://archive.org/details/rommelpapers000270mbp); "Tank Action. From the Great War to the Persian Gulf", by George Forty; "Armoured Warfare", by F.N. Toase and J.P. Harris
I am not sure I agree with the premise of the question. Cold war era tanks were far more powerful than those of the WWII era. Manufacturing limitations in Germany and the Soviet Union meant that the focus was always on ease of production rather than building the massive tank killers that predominated in the cold war.
As the war was winding down, Germany focused more on building armored guns that could be used defensively against advancing tank formations rather than escalating a tank arms war that they simply couldn't win even if their designs were effective.
At some point there are real physical limitations on tank size that cause decreasing returns in effectiveness as armor and larger guns are added and mobility goes down for little combat effectiveness. A bigger gun and armor don't do much if you aren't mobile enough to engage effectively. Modern tanks would simply destroy a WWII era tank. The gap would be even larger than shown in Desert Storm where M1s destroyed the T-72 iraqi tank force.
The development of tanks did not slow down after World War II - it just became less visually impressive.
Some of the greatest influences on Cold War tank design besides World War II experience come from the Arab-Israeli wars of 1967 and 1973. Both conflicts provided proving grounds for designs from both sides of the iron curtain, especially in the Sinai Peninsula.
1967's lightning maneuvers by Israeli tanks (often kit-bashed surplus Shermans or French tanks) showed that division-level armored spearheads were still horrifically effective on the battlefield, providing validation for the next major development in armored warfare which showed itself in...
1973, where relatively modern Israeli tanks such as American M60 Pattons smashed headlong into hastily-prepared Egyptian defenses armed with newfangled infantry-based anti-tank systems (Sagger ATGMs and RPG-7s). Israeli forces suffered hideous losses during the first half of the action, and US tanks and equipment were flown in posthaste to replace those losses.
The Israelis eventually found a seam between two Egyptian armies that they smashed through, encircling the Egyptian 3rd Army and driving on Cairo before the big boys made them stand down so that WWIII didn't start over the Suez Canal.
What the more impressionable world took away from 1973 was that the "Age of Tanks" was over, and that the infantryman had retaken the battlefield from obsolete metal beasts. What smart analysts took away was that tank protection needed a significant upgrade, and that ATGMs and short-ranged man-portable AT were significant threats, encouraging further development in protection that led to what we think of as standard in an MBT (composite armor, ERA, etc.).
Very little of this changed the outward appearance of tanks (with the exception of composite armor necessitating a change to flat panels instead of curved hulls and turrets), hence Cold War developments don't look anywhere near as dramatic as World War II's rapid design turnover.
This doesn't even go into the equally dramatic but visually unimpressive addition of computer-aided aiming and stabilizers that finally put the fire-control advantage squarely in the NATO column. The microchip revolution was one of the single most important developments to Cold War tank design alongside composite armor and ATGMs.
They definitely got better, but not in the ways you are thinking.
Fire control systems advanced considerably along with optics (Thermal/Nightvision).
There wasn't much progress made on armor until composite armor was developed. That is the armor currently on the American M1 and British Challenger tanks.
The U.S. specifically continued development after the war for a short time but due to the cost of the Vietnam war the US missed an entire development cycle and wouldn't upgrade their arsenal to anything using technology newer than what was developed in the 1950's (M48 & M60 series) until the 1980's with the Abrams program. (The Russians rolled the T-64 MBT out in 1967 which was the first to use steel and ceramic combination armor)
http://www.amazon.com/Armored-Cav-Clancys-Military-Reference/dp/0425158365 (Pages 1-3)
This is all I got for you right now but it's a good starting point for research! (Sometimes amazon lets you preview books so you might get to see those pages if you are lucky!)