Here's a tip for getting cheap lightweight base layer tops. It is common to get a shirt as part of the package when you register for running events. I see the cast offs in thrift stores in any large city that hosts events like marathons, 5k's, charity fun runs, etc. Some of the tops are brands like Brooks or Asics and others are promo house brands. They all seem to have decent wicking polyster fabric. The caveat is that many are real walking billboards for the sponsors. The upside is that you can get a shirt for $2-$3 and scoff at sharp branches and thorns.
I found this one today for $3. It is 6.6oz in XL size and not too bad on the front.
Everyone got their ad on the back though:
