I feel that a hunger meter in a fat fetish game is probably almost always be a sort of limiter. ether to make food buffs/healing less abusable or to balance vore. It could also be used to limit leveling if you tie leveling to eating (like in this topic). if a game have a sort of day limit (like in Pikmin) it could lead to an interesting choices between fattening/leveling and healing/buffing.
you could also make it so that being x% full heals or replenishes mana. it would work really well if the game also have a vore move. do you have stay hungry so you can vore more or get full so you can heal?
one other thing it could do is make it so that traveling places with little food lowers your fat level.