Warriors are boosted by the memory of a tense 23-19 victory over Joe Schmidt's men in September that ended the Irish club's record 26-game home unbeaten run.
Since then Warriors have played the Irish province on three further occasions, losing two and drawing the most recent meeting.
And Sean Lineen's side will head to the RDS buoyed by their winning league finale over bogey team Connacht last Saturday.
And Weir is bullish about his side's prospects of making the play-off finals for the first time in Glasgow's history.
Weir said: "We know how good Leinster are, but we also know that if we get it right we are more than a match for them. So we will not be travelling with any fear of facing them.
"We know that we are entering the lion's den, but we have been there before and won and that gives you a lot of belief.
"On top of that, the way we controlled Connacht last week, after the first quarter, is a further reason for us to be confident that we can get the win we need to make the play-off final for the first time.
"It's going to take a massive effort, but it didn't matter who we got in the semis that was always going to be the case. If we can make the final by beating the best team in Europe, it would be all the sweeter."
Perhaps the most relevant of the previous four games between the two sides was the Heineken Cup second leg pool encounter at Firhill, back on January 14, when Warriors threw everything at Leinster but came up just short 23-16.
That was a clash of Test match intensity when Glasgow's inexperience in key areas saw them concede a cheap try and, with the tryline beckoning, blow a touch down in the dying moments when composure went a begging.
The acid test for Glasgow is just how much they have learned from these type of lessons. If they have then we are in for an epic encounter.
But if Warriors are to triumph tomorrow night then Weir will have a massive part to play.
His duel of the boot with Leinster playmaker Jon Sexton will pitch the two most prolific stand-offs in Europe's top league against each other.
Sexton tops the kicking charts with an astonishing 89 per cent success rate, but Weir trails him by just three per cent and the Glasgow No.10 is relishing the prospect of playing a pivotal part in what he hopes will be Glasgow's greatest ever triumph.
Weir added: "The stats don't lie and Sexton is top by rights. His consistency is unbelievable both when it comes to keeping the scoreboard ticking over and also when it comes to keeping Leinster playing in the right areas with the quality of his field kicking.
"Personally, it is great to pit yourself against the best. My focus will need to be total and it will be a pressure- cooker atmosphere, but that is what it is all about at the top level."