Last time out Villa led City's rivals Manchester United 2-0 thanks to a brace from Weimann. However, visiting United battled back to win the match 3-2, dropping Villa to 17th in the Premier League table in the process.
Despite that setback, Weimann believes that the performance his teammates put in against United will have boosted their morale for the trip to City.
"I'm sure that if we play like that we've got a chance of getting something. You saw against United that we were capable of going 2-0 up and we should have got something," he said. "We don't have fear and we shouldn't have. The last few weeks we've got confidence because we've won a couple of games. We know one of those was against Swindon, but as a young team, if you win a game then you'll get confidence.
"I think you've seen the way we played against Manchester United, at the moment we think we can take on anyone and I'm sure next week at Manchester City we'll be the same.
"The training ground last week everyone was buzzing because we'd won two games and it was brilliant. If we can keep playing like that we'll get a few more wins soon enough."
Weimann joined Villa as a trainee in 2007.