15mm climbing tape doesn't hurt trees - I've been using it for a long time and it doesn't hurt the bark in any way, nor cause any depressions in the sapwood and it knots easily and securely. I weight nearly 16.5 stone, so I'd say it was pretty safe
. Ogri is right, there are cheaper options as he mentions. Car seat belt material has been used as well.
Bascially you want something with low stretch - so your hammock doesn't sag to badly under load. Something flat and wide, so it doesn't dig into the tree, will provide maximum surface grip and something that is strong, no one likes getting dumped on the deck by their hammock in the middle of the night.
HTH