Guys, don't make fun of fat people

Guys, don't make fun of fat people;
It's not as if they don't have enough on their plate.

This joke is a fat joke. This is a category of jokes that are fairly common in america. It is also a pun.
The pun part of this joke is the fact that saying someone "has enough on on their plate" is a colloquial phrase that means that they have to deal with a lot of things. It can also be taken literally, and mean that the amount of things that they have on their plate are more than enough.

This brings us to the fat person part of the joke. The fat joke part is saying that fat people eat a lot (which is insulting because it is assumed that they eat too much).