House grew up in a household where “if you were two minutes late for dinner, you didn’t eat.” It follows there would have been other rules surrounding food, likely things like “this is what’s for dinner, eat it or you don’t eat” and “you have to finish what’s on your plate.”
I feel like this would be a possible explanation for why he steals Wilson’s food so often.
House is conditioned to eat whatever is on his plate and finish it. House is smart guy though, and would likely find work arounds to his own issues/behaviours, ie: if it’s not on HIS plate the rules don’t apply.
It would explain why House sometimes eats off Wilson’s plate and sometimes gets his own. If House likes what’s available in the cafeteria and feels he can finish a portion of it he makes Wilson buy him lunch.
However, if he is unsure if he likes what’s available he’ll eat off Wilson’s plate and if he doesn’t like it it’s okay because it isn’t his meal, there is no pressure to eat more.
Same goes for if House isn’t particularly hungry but recognizes he should eat something (could be lots of reasons for this but gotta throw in my personal headcanon of autistic House having poor interoception so he doesn’t always feel hunger, thirst etc but will sometimes go “I haven’t eaten in a while, I probably should.”) and so he tries a bite of Wilson’s food and if he likes it, he steals half. The small portion is more manageable when he is experiencing low appetite and is less stressful to need to finish.