Weight alone is not faster. Bigger, heavier riders that come into this game with bigger FTPs to start are carrying more muscle mass. They have tree trunk legs that can push on the pedals harder but a guy like you probably drops them in the hills.
I do think strength training is great and worth your time.
It does seem to take a while to ramp up with strength training (well, at least for me). I started a few weeks ago and mostly I’ve been doing a lot of conditioning exercises in order to prepare for the big stuff. I just started some of the harder stuff and four sets of walking lunges and step ups with dumbbells left me sore for three days. I’m going to soldier on and do base miles with sore legs this winter in the hope of getting faster. 