Glasgow are looking to defend the title they won by beating Bulls in Pretoria in June.
A young Glasgow side lost 31-0 to Zebre in their first pre-season game and face Connacht next in their final warm-up match before facing Ulster when the real stuff gets started
Weir, who started at the weekend, says the intensity Zebra showed from the first minute demonstrated the challenge facing Glasgow this season.
"Everyone's going to be looking for the scalp of the champions," said Weir.
"It's going to be something that we're going to have to embrace. We can obviously take real confidence from last season, but it is in the past and it's a new team here."
Weir believes the title win is "one of the best moments" in Scottish rugby, but it's now about "biting down on the gumshield" and trying to repeat the feat.
And Weir says Franco Smith has assembled a group that can compete at the top end of the league once again.
"We have some unbelievable athletes, we're well coached, we all know exactly what each other is doing," he said.
"We have a template for every scenario. It means you have the freedom to play your best rugby and put your best foot forward.
"You know your teammate will always back you up. It is a special team and I love it dearly."