Thus: it affects only my damage, and you need to have a high dps weapon, so that you can do dps....Quote from Kisho
You care about your weapon because of enrage timers. Can't rely on your group to cover your slack: you need to be contributing DPS. It really isn't like WoW at all.
In answer to your other question (what does weapon DPS affect): anything that does damage. Heals only scale with your level, or maybe with your max HP. Turn on advanced tooltips and double check, it'll say what it's scaling with in there.
But yeah. You need a high DPS weapon. Don't think like WoW!
Yeah, so in other words, as a MonkTANK, since I'm running with 3 RL friends all the time who are doing ridiculous DPS, theres no need for a high damage weapon?