I don't cook at home much, so my refrigerator is always pretty much empty. Should I get groceries or leave money for groceries when I have a dogsitter staying at the house? Just not sure what's customary.
As a generalized rule, a house sitter is going to bring whatever personal items they need/require, which would include food. You need to provide accommodations, like clean bedding, towels, etc. Sometimes it can be nice to leave some special snacks for a sitter, but you should let the sitter know they're for him/her. A sitter would not automatically think they could help themselves to your food unless told specifically.