Weir has recently signed a new contract at Ibrox after making 61 appearances for the Gers in last season's bid for four trophies.
"I hope I get the opportunity to play another 60 games," the 38 year old told the Daily Record.
"Having that amount will mean it has been a successful season for the club and that would be great for me. You just don't know what's around the corner in football, but I want to play 60 games and I think I can play 60 games.
"I'm sure there will be other players coming in and providing competition, that's the nature of Rangers, but it's up to me to try to get into the team.
"You have to earn your place every week and you have to have that competitive nature.
"It's going to be tough, but that's how it should be. It's like everything else in life. You can look at it negatively or positively and I try to be a positive person.
"Motivation is not a problem because I love the game and I enjoy it.
"The motivation comes on a daily basis trying to prove yourself and keep up with the young boys. It's self-motivation because if you need someone to do it for you, there is definitely something wrong."