My pump tank has a leak in it, and so needs to be replaced. The current tank is a 36 gallon tank, similar to this one. Is there any risk in upgrading to a 52 gallon tank, such as this one? I would think the benefit would be that the pump would have to run less often, but I'd like to have clarification on that too.
A larger tank will cause the cycles to be longer (slower), but overall the runtime will be the same (if you use 500 gallons of water, the pump has to supply 500 gallons of water). For example, if the tank is full and you open a tap, with a 36 gallon tank it may take 60 seconds before the pump starts, and then 30 seconds to run, and repeat. With a 55 gallon, it may take 90 seconds before the pump starts, and then it will run for ~50 seconds. In both cases, this is ~33% duty cycle (if you excuse my rounding errors for simplification), and so if you leave the tap open for 10 minutes you'll get a total of 198 seconds or 3.3 minutes of runtime.
The downsides to a larger tank are simply that it costs more and takes up more space.
The only real problem is if you have too small of a tank you'll cause the pump to cycle too quickly which wears it out faster.
Your well-pump should be sized to match the "make-up" (the speed at which water flows back into the well). That being said, bigger is better for your pressure tank. What kills well-pumps is starting, it takes the most abuse from starting, so running is the least work. So to have a larger tank means fewer starts and longer run times, and it also means more available volume and stable pressure in the water plumbing.
So short answer is there wouldn't be any risk as long as your pump is sized to the make-up of the well.