Assuming a steady surplus of 500, and considering that a kg of human fat is roughly 8000kcal, it will take two weeks to gain a kilo. But a larger person consumes more to simply stay alive so the curve flattens out once a certain mass is reached.

Excess means above what your metabolism consumes. If I'm 200 pounds and my metabolism consumes 3200 calories per day, eating 3200 calories per day isn't 500 calories in excess. Same as if I'm 600 pounds and 4000 calorie metabolism. It isn't excess unless its excess.