The 40-year-old defender has signed on for another year with the Scottish champions and believes the forthcoming campaign will yield further success for Walter Smith's men.
Rangers secured a domestic double last time around and Weir says the squad will return stronger than ever thanks to an extended summer break.
"We've still got the memories of winning the league so we all want to do that again," he said.
"The memories are still fresh in the mind and we know this is where it starts, the build-up to try and achieve that again.
"Those memories are still there and that's what keeps driving you on.
"We had a substantial break this year, which is unusual, and hopefully we will get the benefits of that.
"The players with niggles and a few knocks can get rid of them and come back fully fit and hopefully stay fully fit for the season."
The squad at the moment is more compact than usual following the departures of Kris Boyd, Nacho Novo, Steven Smith and DaMarcus Beasley, with Smith yet to add to his group over the summer.
"It's part and parcel of football," said Weir.
"It's sad to see the likes of Kris and Nacho, Stevie Smith and DaMarcus leave, lads who have all contributed and played a big part.
"But when you're involved in football for any length of time you quickly become accustomed to that because that's how it operates.
"Nothing lasts forever and you've got to move on. It gives opportunities to other lads to come and fill the positions.
"With Kris going, a lot of goals have just disappeared but there are lads who can come in.
"Andrius Velicka is fit again, Steven Naismith is fit again and looking good and Kenny Miller and Kyle Lafferty have contributed goals-wise as well.
"We have options and it's a great opportunity for those lads to go and make themselves top scorer."
Weir also believes more stars of the future can follow in the footsteps of Danny Wilson and John Fleck by making the breakthrough from the youth ranks this season.
"It's a great opportunity for them," he told Blues News.
"They are involved in the first team group and they are closer than ever to the first team. It stimulates some people and can really be the making of them.
"It's a great opportunity for them to do that, to go and grasp that chance with both hands, as Danny did last year and John Fleck has done in the past.
"It's a chance for them to become a fixture in the first team and to be a Rangers first team player."