I used to think it was heavily in Rosa's favor before the Charizard buff hurricane started going on; now I'm not too sure. Flamethrower puts a hamper on Luma's effectiveness since it can flinch and it covers most of Rosa's approach options with Luma pretty well; and the fact 'Zard now has a reliable combo throw on top of his already fast grab definitely makes handling Rosa easier than before. Having a reliable kill throw also really helps the MU for Charizard. Luma himself is very much vulnerable to many of 'Zard's attacks; especially his jabs and aerials; I'd reccommend keeping an eye on Luma so that Charizard doesn't have the chance to inflict some major pain on the little guy. Rock Smash's super armor also causes issues for Luma.
Charizard is a character that preys on getting in somebody's face and pounding on them, which Rosa isn't the most well-equipped to deal with without Luma to wall Charizard out. Flamethrower (IIRC, at least; please correct me if I'm wrong, Rosa players!) beats out Luma Shot, which makes it a bit harder to use in the default MU, but Rosa definitely has the advantage of having two whole entities to work with, which could make combos a lot easier on Zard when Luma's in play. Fly is also pretty damn bad for Luma to get caught in, and Fly's also a very reliable OOS option on Rosa herself. Her lighter weight definitely means she'll need to play a very cautious game, since it takes more damage for her to get Charizard KO'd then it will take for Charizard to KO her.
He's still a big target, and the fact that he's a heavy is always going to be an issue...but I think the MU's a little closer to a 50/50 now in non-customs. Maybe 30/50 as opposed to Rosa dominating Zard 90/10 like at launch.
With customs, I think it really is an even 50/50. Customs greatly enhance Charizard's ability to get in on Rosalina, with Dragon Rush making for a solid recovery option and a good grounded option that does even more damage to Luma than Flare Blitz does (thanks to it being a multi-hit move) if Luma gets caught in it. Luma Warp is a dangerous asset to Rosa since that move basically negates the issue of Luma Warp getting blocked by Flamethrower, though; however, a simple dodge or a hard read can remedy that.
Charizard is really so much better than he was at launch in this MU, especially with customs.