The 23-year-old underwent surgery in January to repair his right biceps, ruling him out of action for up to four months.
In his absence, the Warriors have continued to be one of the pace setters in the league and currently sit top by four points with five games left.
Last year the Warriors made it all the way to the final, before losing out to Leinster 34-12.
Weir himself was not picked for the final while he was ruled out of their play-off bid in 2013 due to a broken leg.
But with progress being made on his current injury recovery, the Scot insisted admitted he was eager for a return to action before the regular season was up.
"If I can make the Cardiff game I have four games before the semi-final and final," Weir told Glasgow's Warriors official website.
"It's a huge goal of mine to work my way back into the squad to help push the team forward and get that first title.
"We came so close last year, and I think we have learned a lot from the agony of losing in that final.
"If we are in a position to take a bunch of supporters over to Belfast, just like in Dublin last year, it will make for a great atmosphere."
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