... how strong a character is, and the weight of what they're pushing must come into it surely? Yes, but... We can account for that and still keep it simple and approachable using the elements already defined for regular use within the system, without bringing new elements in. For starters: it's impractical to introduce maths or scales relating to character weight that both realised on an aspect of a character's weight that will give some races a heavy disadvantage compared to others (something they wish very strongly to avoid), [...]
Instead... Many class features already take into account size category of the target creature - and size category and weight go more or less hand in hand anyway, most of the time. So, what we do instead is say that you can only shove something that is no more than one size category larger than you - something bigger than that is, by proxy, going to be too massive and too heavy for you to effectively shove. This is how that is accounted for and worked into the consideration without making the whole mechanic more complicated... and it works well for doing that, the majority of the time.
It always baffles me that creatures 1 size larger than you don't get advantage to resist grapple & shove checks (and/or advantage on shoving a smaller creature). The Enlarge spell grants characters Advantage on strength checks, but simply being 1 size larger naturally doesn't...? I recognize that this is probably for balance purposes to prevent small PCs from being underpowered, but it still feels weird. (I would prefer if larger creatures got advantage on STR checks, but smaller creatures get +1 AC as in 3.5e).
