Train harder, ride faster. Lose the weight if you can ... But what if you Do lose the weight, and find that a few percentage points change is insignificant on those hills .... i.e. you have to get off and walk ten yards further uphill?

Train harder, or with better focus, .... do HIIT and hill repeats, maybe even add some leg lifts in the gym.

As for people hating fixies .... LOL a think-skinned New Yorker. Didn't know they made them.

Ride what you like, like what you ride. You want to climb hills, train to climb hills.