The heavy (heaviest I can find-usually Eddie Bauer or Lands End) is so it retains more water after I wet it and for a longer period of time. Around here (dry heat) a thin long sleeve T-shirt will dry completely in about 15 minutes of riding. You are COLD for 15 minutes though ;-). I MUCH prefer to be COOL for a couple of hours at a time. The turtleneck is so it cools my neck area also. I am talking about the mesh jackets-I prefer the First Gear Mesh-Tex, but Joe Rocket Phoenix and some others are very good also. This keeps the shirt from drying out too fast as well as providing the protection in case of a crash or impact. My family owns three mesh jackets. My favorite place to get them is
http://www.newenough.com especially on clearance when they are $69 or even $49 like the last one I bought. I also have the Joe Rocket mesh pants-First Gear doesn't make my size ;-( These are very cool and protective. They also let me pack far fewer pairs of pants on a long trip.
http://www.aerostich.com/riderwearhouse.store and type "cool mate" into the search box. This is a great product and will nearly freeze you out!
I do switch to a thinner long sleeve T-shirt under my jacket when traveling in high humidity areas. The turtleneck will not allow enough evaporation in those areas.
I hope this helps.

BTW-I am quite comfortable riding in 110º-120º heat with this set up. East of the Mississippi (high humidity-like south Texas!), this will make 100º nearly bearable as long as I can keep moving.