Warriors struggled to play with their usual rhythm but eventually came out on top to win 38-26 after trailing 12-16 at half-time.
Weir believes that a home quarter final back is a chance to show their quality again.
"I can't wait for next weekend. Getting back here at Scotstoun, it'll be another great occasion," he said.
"We're a free flowing team and an attack and if we can nail our basics, the little one percenters that often the punters won't see, but we'll know if we do all those little jobs cleanly, then ultimately we'll get clean ball and we'll get tempo in our game.
"Sadly we didn't get that at times today, but we'll look forward to learn going into next weekend."