The 21-year-old will start at fly-half against Bath at Old Anniesland on Friday night, as Franco Smith's squad complete their pre-season preparations ahead of the new campaign.
Urwin signed his first professional contract with the Warriors in March, graduating from the club's academy setup after impressing at age-grade and A level.
Now part of the senior squad, the stand-off has continued to develop under the watchful eye of Weir, who made over 150 appearances for Glasgow before moving into his current role within the club's academy coaching setup.
Weir believes Urwin's understanding of the game has developed significantly during his time in the academy.
"From when he first came in to now, his rugby IQ and the way he reads the game has improved massively," Weir told Scotland Rugby News. "I think that's just down to his three years in the academy and all the hard work with the under-20s exposure that he's had throughout the years. It has led him to a point where now he can read the game really well for such a young player, which is amazing.
"Obviously, he's got a really high skill set to back up that rugby IQ, so when he does see a space or he does see a cross-field kick or whatever it is, he's got the skills to back up and execute. Which probably at a young age you would expect to have one and not the other.
"I think he's got a really bright future ahead of him, and I'm really looking forward to seeing him really grasp as many opportunities as he can. Because every A game that he played in last season, I thought he looked head and shoulders above that level. It looked like he's completed that level of rugby, so his next challenge is to step up to the first 15."
Urwin will be looking to compete with Dan Lancaster for opportunities at stand-off during the 2026/27 campaign, with Weir confident the youngster has the foundations required to make his mark at senior level.
Asked whether Urwin can push Lancaster for a starting berth, Weir replied: "Definitely. I think three years in the academy has given him a really solid foundation of how the coaches want to play and the philosophy behind everything.
"Like I said, I do think he looked head and shoulders of being really comfortable and really outperforming in the underage games. I feel like that was a level that he really has conquered.
"He didn't look like he was learning during those games. I thought he really stood out in all aspects of his games. I'm really excited to see how he goes.
"Obviously, he is a first team member now, which is great that he graduated out of the academy. It's always been nice for me to just, like I'll always keep in touch with all the kickers and all the rest of it anyway at training to have a touch point there. He's a great lad and I do believe that he'll go on and do really well this season."