Are you "mirroring" to the external display? If so, don't, drive it independently doing what Apple calls "extended desktop." In fact, learn how to run it closed lid so you direct all your resources solely to the projector. A 2010 MBA shouldn't have any problem with 1080p as a desktop resolution on an external display or projector.
However, just so you know, the Core 2 Duos in that generation Air aren't super powerful, you may actually have some trouble with full-size bluray rips even if you use XBMC, a much better software player for the task, than VLC. The 2010 Minis with the same Nvidia GeForce 320M can handle it, they were 2.4/2.66 C2Ds though and had plenty of oomph, my MacBooks and Minis in that 1.8-2.2 C2D range could not reliably do full MakeMKV blu-ray rips perfectly with XBMC. It wasn't until the i5 that entry level consumer Macs could handle bluray perfectly, and could do so without any graphics assist.
So, so don't mirror, do extended desktop to get 1080p, test playing your bluray rips at 1080p to your projector with the lid closed, and then reassess. I'd use XBMC or Plex rather than VLC.
Just so you know, home theater and watching blurays with a computer is MORE of a hassle than using a bunch of standalone consumer electronic devices, not less. So if you're not prepared for some hassle, best not to get too deep.