Someone who's paunchy has a round belly. If you're more paunchy than you used to be, you might want to invest in slightly larger, more comfortable clothes.
This adjective is often used in a mildly derogatory way, to describe someone who carries a bit of extra weight around their middle. Has your vet put your dog on a diet? It might be because she's gotten a little paunchy. The word comes from paunch, "round stomach," from a root that simply means "belly or stomach."