It was the first time supporters had been inside Scotstoun since February 2020 and Weir gave them something to cheer on his return to the club after five-and-a-half years away.
His 18th minute try was reward for a fine performance but Newcastle hit back in the second half with tries from Callum Chick and George Wacokecoke.
Weir looked eager to make an early impression but an attempted interception was knocked on and allowed Newcastle to pin back Glasgow in their own 22. The Warriors stood up to a sustained period of pressure which was eventually relieved by Weir’s booming kick into the opposition 22.
Johnny Matthews thought he was in for an interception try only to be hauled back by referee Hollie Davidson but the Glasgow hooker got another chance a couple of minutes later and this time the break paid dividends. Matthews made the most of a turnover, surging into the Newcastle half before Stafford McDowall played in Duncan Weir who ran in the score between the posts, then converted.
The visitors were reduced to 14 men five minutes later when Glasgow scrum-half Sean Kennedy was taken out by Will Welch after he chipped over the Newcastle flanker who was sent to the sin-bin.
It was the cue for the home side to open up and although the backs moved the ball well they were unable to add to their lead before half-time.
As promised, Danny Wilson made a mass substitution after 51 minutes, changing 12 of his side, with a couple more changes following ten minutes later.
With Newcastle also utilising their full squad the flow of the game was inevitably disrupted but the visitors managed to draw level with 13 minutes remaining. A fine interception try from England cap Chick saw the No 8 sprint 30 yards to the line despite the efforts of George Thornton to haul him down. Will Haydon-Wood added the extras.
Newcastle nicked the win in the final minute when Wacokecoke outsprinted the Glasgow defence to touch down in the corner.
Scorers: Glasgow: Try: Weir. Con: Weir. Newcastle: Tries: Chick, Wacokecoke. Con: Haydon-Wood.
Glasgow: 15 Ollie Smith; 14 Rufus McLean, 13 Sione Tuipulotu, 12 Stafford McDowall, 11 Ratu Ragive; 10 Duncan Weir, 9 Sean Kennedy; 1 Tom Lambert, 2 Johnny Matthews, 3 Murray McCallum, 4 Lewis Bean, 5 Richie Gray, 6 Kiran McDonald, 7 Rory Darge, 8 Ryan Wilson.
Substitutes: George Thornton, Grant Stewart, Murphy Walker, Rob Harley, Max Williamson, Scott Cummings, Thomas Gordon, Rory Jackson, Jamie Dobie, Ross Thompson, Logan Trotter, Peter Horne, Finlay Callaghan, Cole Forbes, Nick Grigg.