Brother SamG:
As GTs58 says, the classification is all about tire size. 26 X 1.75 is a middleweight. 26 X 2.125 is a ballooner. The difference in tire size has no relation to load-bearing capacity. That is a function of the design and manufacturing of the frame and other components. Some frames have reputations for sturdiness, like some Chicago-built Schwinns. I'm sure that you could get a range of opinions about that on this forum. Your edit shows that you understand that intended use is important. A bike that survives slow, casual riding may not hold up jumping curbs or doing wheelie hops. Have fun!