Warriors stuttered to a 38-26 win over bottom side Zebre on Friday and speaking after the match, and before Stormers were confirmed as their opponents, Weir told BBC Scotland: "Whoever we're playing next weekend we know we need to go up a couple of gears and we've got it in our squad.
"It's not a panic, it's not kind of all hands on deck and we need to kind of reinvent the wheel.
"All the solutions are in the building. All the solutions are with the coaches and with the players themselves.
"We will go and review it and we'll definitely be better next weekend, that's for sure."
Weir led the Warriors alongside his children to mark his 150th appearance for his hometown club.
"It was class," he said. "As soon as the team got announced during the week we stupidly told the kids and they've been asking when do they get to go out in Scotstoun and run out in front of all the flags and the fans.
"My wee one Emily was up during the night last night, but thankfully my wife Nicola took the brunt of it and gave me the full night's sleep.
"It was a special moment, one that I've been itching to achieve when it was creeping closer, and it's special doing it at home with the kids. Brilliant."