That's me at the gym today after a 15 minute run and in the middle of a dumbbell curl/overhead dumbbell press/hammer curl 12 rep superset with 20/35/20lb dumbbells. Completely relaxed.
I was 226lbs back in July 2011. I had basically stopped exercising for two years. I picked it back up, lost 20 pounds then sprained my ankle badly Thanksgiving 2011. Couldn't run and didn't lift a whole lot until March 2012. Ballooned back up to 215.
Then I rededicated myself. And for the past year I've been doing low weight, high rep and supersetting everything. I do each body part twice a week. I ran a marathon in November, and will be running another in three weeks. My weight has been 200lbs give or take 2-3 pounds since November. I've been adding lean mass and losing fat. Sounds unbelievable, but when your clothes are getting bigger, you know you're doing it right.
So yeah, heavy weights for size aren't a necessity.