Yes, this is a thing that can happen. When temperatures are high the air density means that planes need to achieve a higher speed to take off. Same for increased weight. Same for high altitude airports. Same when there's less headwind to take off into.
If enough of these factors are bad enough, you have to change what you can. Can't change the airport elevation or the weather, so that leaves you with the weight.
You realize localized weather is not always predictable far enough in advance to do much? Moreover, airlines don't require passengers specify their weight when they purchase a ticket, so they can't really plan ahead for going over a specific weight that is itself tied to local weather conditions. Mind you, this could be avoided by building in more wiggle-room, but that is not going to be accepted as a solution because it results in waste much of the time if, for example, you have empty seats because you wanted to be sure that you wouldn't run in to the issue of going over weight.
Kick of the heavier passengers and they don't have to remove as many total people. Which is overall better as you're creating travel problems for fewer people.
Although unless you're like 20st then it's unlikely that it would matter a great deal whether you pick the weightier people since they'll be making the calculation based on a formula that attributes a set value to passenger weight.