Warriors opened their campaign with a bonus-point victory over Sale Sharks at Scotsoun last weekend while Toulon went to South Africa to claim an impressive win over Stormers.
Speaking to BBC Scotland, Weir said: "It's about just making sure that the best version of the Glasgow Warriors go out there.
"Not getting [swept up in] the atmosphere too, it's an amazing place to play.
"I played there, I think it was in 2013 away at Toulon, it's such a cool environment with the little chant they do before the game and all the rest of it, so it will be about us and how good we are at implementing our gameplan on to them and just staying relaxed and really enjoying it as well.
"Our away form's been good, it's been really pleasing to see that and how it's come on, we've got that great win out in Cape Town as well against the Stormers."
On Toulon, Weir added: "They've been in a good, rich vein of form this season as well, so we know it's going to be a hard challenge.
"They're obviously big men, similar to Sale, but they've got some superstars in there as well. It's going to be a good task to see where we can match up in this competition.
"We got a lot of credit for Saturday's performance, but it will be nice to test it against another really good side on Sunday."