Why was my carrot cake very heavy?
If I had to guess, I'd attribute it to the huge amount of stuff that's in the batter, which makes it more like a fruitcake than like a traditional cake.

You only have two cups of flour but you have four cups of carrot, coconut, raisins and nuts. This is definitely going to make a very dense cake and it sounds like it's supposed to.

This is pretty common in carrot cake recipes but it's not required. I recommend that you find a recipe designed to be more cake-y (higher flour to stuff ratio) rather than trying to fix this one. I've been really happy with the carrot cake recipe from Cook's Illustrated/America's Test Kitchen but it's behind a paywall.