The Austrian international, who joined the club six years ago as a 16-year-old, believes the current squad are only going to get better.
And with Lambert ready to strengthen his side in the summer transfer window, Weimann, who is in the final year of his current deal, is excited about the future.
He told the Daily Mirror: "What the gaffer is building here we all believe in and we just have to continue working hard for him and each other.
"I think that's what Aston Villa is about. It's a family club.
"We're growing and getting better all the time, and I think there's a lot of potential in the team right now because as players we're only going to get better.
"Like I said, the spirit and belief within the squad and within the club is really good
"It's really exciting for everyone, it's exciting for the players, it's exciting for the fans and it's exciting for the club.
"The club is very tight-knit. A couple of weeks ago the chairman was here watching training, chatting to the manager and the lads and that's the way we are, everybody very close.
"I've been here for six years now and I've loved every minute of it."