Two people is too much!!! It happened here just recently. If it's the black webbing, then yea it can break when someone else piles in the hammock with you, especially if its worn. For two people, you have to have something more robust than typical cottage ultralight webbing.
I have pissed my girlfriend off several times because I refuse to let her in my hammock with me. She's not going to ruin my tree straps.