The timing depends on the size of the internals, but broadly speaking, you'll accumulate weight constantly while someone is inside. The weight gain speed is about equivalent to a round of food-digestion (4 pieces of food, or 2 slices of garlic bread) every 145-220 seconds, depending on the prey's size.
It's not fast, but it's enough to make a noticeable difference when someone stays in there a little while.
Eating food and rubbing the belly doesn't change the vore digestion, but you'll also gain weight from the food you eat- the feeding and vore weight gain systems can both work at the same time.
Also to be clear, there's no concrete "end point" to the digestion- it just lasts until you decide to spit the prey out, or they decide to hop out of the chair. If you want to play with the sentient fat/ ghost hands system, the prey can just change into the ghost hands avatar and hop out whenever the two of you feel like it's been long enough.