I don't know scientific evidence, however my roommate is 120 kg and only about 1.75 m tall(so yea, he's really fat) yet he has a LTR going for over 3 years and got a couple booty calls that I know off only in the past half year we've been living together. So I'd say looks might have an initial impact, but you can definitely push yourself in with game alone.

Do looks matter?

Yes. Drill it in, accept it, move on. I'm not gonna restart this age-old debate because the answer is obvious.
Women fall into 3 cathegories. Receptive, unreceptive and neutral. Looks don't affect your entire game in general, but it will affect the amount of women that will be receptive toward you before you even open your mouth. If she's receptive, all you need to do is not fuck it up. Simple as that.

Neutral ones are where so called "game" comes into play. You have to polarize her and get that attraction going until she becomes receptive. The idea with neutral women is that they don't stay neutral for long. And the longer it takes you to make a move, the more she'll drift into the "never gonna fuck you zone".

Unreceptive girls are a waste of your time. You can be the smoothest Rico Suave that ever walked the Earth, every once in a while you'll come across one of these. The time and effort necessary to shift her is not worth it. Simple as that.

Now before you go crying into a corner because you didn't win the genetic lottery, wait for the good news. It doesn't take much for a man to be good looking. Sure not everyone has a jaw that could cut diamond, but everyone can buy fitting clothes, get a good haircut to match their headshape and subscribe to a gym.

looks alone will not get you laid. If you are the best looking guy in the world but have no personality, you are not getting laid.

good looking + personality = laid
ugly + personality = laid

also remember beauty is in the eyes of the beholder. some women like hairy guys, some women like bald guys, some women want nice teeth, some women want a 6-pack.