Ultimately although better designs and extra horsepower may improve mobility, in many terrains operating ultra heavy vehicles is just straight up impossible. No matter how advanced technology gets, the same watery beach or muddy slog does not suddenly get extra supportive strength to keep you from sinking in. In WW2 the black panthers weighing 45tons mobilized well with many terrains but Tigers at 55tons often get stuck in mud. Tiger 2 weighing close to 70 tons breaks the ground wherever it goes.
AFV mobility is quite often misunderstood.
First up, the Panthers (Pz.Kpfw. V), Tiger I (Pz.Kpfw. VI Ausf. E) and Tiger II (Pz.Kpfw. Tiger Ausf. B)
ALL had good floatation or soft ground mobility.
The Tiger II didn't break ground wherever it went - no more so than the Panther or Tiger I did as they all had similar suspension design and similar gross metrics on various aspects of ground pressure. All 3 tanks actually travelled well over soft/muddy terrain but did often get "stuck" in mud because they all used interleaved road wheels which were susceptible to being "stuck" together if the mud hardened or froze them together.
To understand this, consider first that the average tracked vehicles, despite being significantly heavier than wheeled vehicles, are often viewed as having better cross-country mobility than wheeled vehicles. This cannot be if tracked vehicles often "break the ground" and become immobilised by virtue of weight alone. Weight is one of the factors but is not the determinant here.
Ground pressure (GP) is often used as a rule of thumb mechanic in that weight of the vehicle is divided by the contact patch on the ground which determines how much pressure is being exerted on the ground. Take an example of a human standing on deep snow and sinking into it. Same human, weight remains same but now with snow shoes. Contact patch has now enlarged so weight per cm2 is now reduced and said human stays "afloat" on top of same patch of snow. Same principle applies to vehicles.
MMP or Mean Maximal Pressure or VCI (Vehicle Cone Index) is a slightly more complicated measure of ground pressure. The basic of this is that pressure along the track is not evenly distributed (which GP assumes). There are peaks that exceed nominal GP due to the contact between the tank and it's tracks being via the road wheels. The bigger the contact patch between road wheels and track, the more evenly distributed the GP and the lower the MMP. Logically, to achieve maximum contact and lowest possible MMP, you need lots of small wheels (think caterpillar tracks or Churchill Tank). However, small wheels are bad at high speed. For high speed, you need bigger wheels but bigger wheels means smaller contact patch, leading to higher MMP which means that section of the track breaks through the ground "crust" causing the rest of the track to start sinking into the terrain. Hence the German design of interleaved road wheels for the Big Cat series of tanks. Same example of human, this time lady in stiletto heels. Standing still, GP is divided across the heel and ball of the shoe. But walking, when the stiletto strikes the ground, before the rest of the foot does, the weight is exerted over that little point. So MMP here is waaaay higher than the Nominal GP.
To summarise, weight alone is not a determinant in the
tactical mobility of a vehicle and how it will perform in soft ground. There are tracked mining vehicles at 10,000+ tons. Design of vehicle suspension and trafficability of ground (single pass vs multi pass) can totally change the picture.
Weight though is a very big factor in the
strategic mobility of vehicles (within operational context). As has been often pointed out, the ability of the road infrastructure (primarily bridges) to accommodate repeated traffic from 30 ton and 70+ ton vehicles is vastly different. If a bridge can only take 30 tons, your formation of 70+ tons MBT is going to come to a grinding halt. Which is why you see so much emphasis on bridging assets in armoured formations.
Another less limiting factor is size of vehicle. Width is a factor that also affects strategic mobility (ex-theatre) in that some vehicles are too wide to rail transport (eg, the Tigers both had specific narrower tracks to fit within the max width of rail transport) and therefore move long distances. Width can also affect tactical mobility as some vehicles are also specifically designed narrower to fit within certain specific quirks of their AO (or even bridging assets).
To gloss over the "mobility" of a MBT by just looking at their gross weight is just wrong.