The antonym for the phrase "grow thick" would certainly be "thin out." When it comes to describing plants, "growing thick" refers to a dense growth of leaves, branches, or stems. Conversely, "thinning out" implies that the plant in question is having its density reduced, either by trimming or by shedding some of its leaves or branches. When we talk about things other than plants, "grow thick" means something is becoming denser, more substantial or large, while "thin out" implies that quantity, size or density is getting smaller or lesser. Thus, "thinning out" is the opposite of "growing thick", which means the plant is becoming sparse, thin or aerial.