Firefly and Aliens Share the Same Universe

An easter-egg in Firefly's pilot episode reveals that it takes place in the same universe as the Alien series. It appears the anti-aircraft cannon Mal uses to shoot down an Alliance fighter was manufactured by Weyland-Yutani Corp.

So does this mean Weyland-Yutani provided the Browncoats with weapons to fight the Alliance? Whose side do you think they were on in the Unification War?

(Firefly,