I am not particularly fond of Gesso with watercolor.. it just doesn't look 100% right and if you rub long enough it can wipe right off
. Having said that, you can try "setting" the watercolor with a gel medium, or PPA or some sort of sealer to "protect" the watercolor.. then you can work on your next layer. Try it! If you are working on paper and not canvas, why not work on watercolor paper..? Don't put gesso down in between the layers as it will wipe away all your work and make everything white! Gesso is used as a primer.. so to erase mistakes, to change colors etc.
It's probably streaky because of it being over the gesso. Let me know what you are working on.. what substrate.. paper, canvas, wood?