I'd say they may be loosely connected. Paul W.S. Anderson was the producer on Death Race 2, Death Race, and Alien vs. Predator. It's likely that including Weyland Corporation in Death Race 2 was an homage or in-joke, but there's nothing to say that it's not the same company (and therefore the films share the same universe).
It's also worth noting that Weyland-Yutani appears briefly in both Firefly and Angel. These shows were created by Joss Whedon, who also wrote Alien: Resurrection. Again, this is also probably an in-joke or Easter Egg, but worth mentioning.
Weyland-Yutani also appears in numerous other media, as in-jokes or visual references. The only one of these I can cite here is Red Dwarf, but you can see visual references to the Alien franchise all over the place.
Weyland-Yutani was a client of Wolfram & Hart in Angel - http://home.vicnet.net.au/~kwgow/cross_key.pdf
In the opening episode of Firefly, one of the characters fires a turret manufactured by Welyand-Yutani - http://firefly.wikia.com/wiki/Weyland-Yutani
A Weyland-Yutani ship appears in the spaceship graveyard in the Red Dwarf episode Psirens - http://home.vicnet.net.au/~kwgow/cross_key.pdf
It's also worth noting that the OP is not the first person to spot the connection. Empire Magazine's article The Most Evil Movie Corporations specifically states one of Weyland-Yutani's corporate activities as "operate privately-owned prisons with scant regard for the health or rehabilitation of inmates."