I agree with Lulu, we put in one offer and one offer only as that was our best offer and it happened to get accepted.
I would tell the RE agent if he wants it sold, then he can put in the whole $2k, and that the last offer was your best offer and leave it at that. Sounds like you aren't competing against anyone else - they don't have any other serious buyers, otherwise why would he keep coming back to you and pushing you for more money?