The former England U21 stopper penned a six-month deal with the Dons on Monday after being released by Sheffield Wednesday.
Weaver is keen to get some game-time under his belt but the 34-year-old knows he will have to work hard for any opportunities that come his way.
Weaver said: "I want to play but I'm sure Jamie will have something to say about that.
"He's been the number one here for quite some time and he's obviously a very able keeper. I think he played just about every game last year.
"I'm under no illusions. I don't feel as though I'm going to walk straight into the team.
"All I can do is my best in training. If and when I get an opportunity, it's up to me to take it."