I made some dinner rolls yesterday and it was underproofed, the result was a dense dinner rolls and it is heavy, does proofing time affect the density of the finished product?
Yes, under-proofing is an excellent way to ensure a dense loaf.
When we bake too soon after shaping (i.e. under-proof our loaf), our gluten network has not had sufficient time to relax. As a result, rather than stretch as its internal gases expand, the gluten simply tears. Under these conditions, gases don't escape in a controlled manner like they should; they burst out at random weak points in the crust, resulting in bread that is over-expanded around the edges, but dense and gummy in the center. Improper scoring (or forgetting to score entirely) can lead to similar end results as the dough desperately tries to find avenues of expansion.
That whole article is a good read, especially in ways to avoid proofing problems. The poke test is your friend. Using your finger (some bakers insist on a floured finger), poke an indentation in the loaf just shy of about a centimeter deep. In a fully proofed loaf, the indentation will stay and you are ready to bake (the indentation will fill as the loaf bakes). In an under-proofed loaf, the hole will bounce back pretty quickly.