Tighten 'er Up!
You are right, the tighter it's hung, the less "sag" factor I've found in the netting. I don't think you'll damage anything unless you bear down on it "too much". What's too much? Well, when I'm inside and I can easily slide fingers/my hand between the netting and ridgeline, then it's not too tight. In addition, if It's too tight I don't get ENOUGH sag in the hammock body itself.
YMMV! In fact, someone with more experience than I have might shed a little light on whether I'm off base. Keep hangin'...I discover new tricks and stuff all the time, thanks to folks on this site and WB.
-- Funny Money
Love 'em while you got 'em