How do airlines ensure that they don’t go past the weight limit?

I’ve noticed that, especially certain airlines, you don’t always have to prebook your cases. You can go to the airport and add them on then, and then weigh them and you’re good to go.

In my mind, what if everyone does that and then the aircraft is carrying a lot of weight…too much weight?

Is there some sort of limit they can’t go over? Would they let on more weight than they’re supposed to?