Quickest way to gain weight on your butt and legs?

You can't specify: Where weight will be deposited. Some will likely go to butt and legs if you have overall weight gain. The best way to ensure ^'ed weight to butt ; legs is by working out with a trainer. Work specifically to develop mass on butt and legs.

Gain muscle mass : Gaining overall weight will add some to your bottom and legs but not necessarily in the manner you want. Genetics play a big role in the shape of different body parts and you have to work with that and have reasonable expectations. To gain bulk but not fat in those areas work on strength training exercises that focus on those large muscle groups. Nutrition also plays a role in gaining muscle mass.