Absolutely they do. I feel I'm always being dumped for the thin ones!
I'm a bigger girl myself, I do try and eat well and I exercise a lot. I'm now more toned but not that much smaller (getting there very slowly)
But, looking at the types of women all my friends are with they are all TINY. Like, size 4 tiny. Little boobs, little waists, little everything!
All men like different women. I mean, I don't like well built muscled guys, I much prefer tall, slim, and natural, but apparently women generally like a ripped man? My ex is about 5 foot 10 and weighed roughly 50kg. Small does not mean unattractive.
If you're frame is small anyway, even if you did put on weight it might look odd. If you look in proportion and normal that is what men like. Symmetry. Don't beat yourself up about it - if guys aren't asking you out it's more because they're scared you're too good for them ;-)