What does "fill up on something" mean? Should I always use preposition "on" to use a drink with this expression?
Very good question. The term "fill up" means to have a sufficient amount to make full/full up. Generally when we are talking about food and drink the preposition "on" is used. So if you fill someone up, or if they fill up, they eat enough food so that they no longer feel hungry. Ex: If we fill up on dumplings we won't have room for dessert. Ex: I shouldn't have filled up on cakes at lunch. I feel sick.