V speeds
 

I have been searching for this answer about V speeds and aircraft weight, I have found that V1 decreases with weight, Vr increases but does V2 vary with weight?

Yes, V2 increases with increasing takeoff weight (increasing Vs, Vmca)

V1 will also increase with weight, since it's not just the accelerate-stop distance (e.g. field limit weight) you have to worry about. Passing V1, the airplane has to be able to maintain the centerline and accelerate to Vr with one engine inoperative. CS-25 requires that V1 is at least equal to Vmcg (minimum control speed on the ground), and the Vmcg just as Vmca (minimum control speed on the ground) increases with weight.

V2 again increases with weight, since it has to be equal to at least 1,13 * Vsr (reference stall speed) and 1,1 * Vmca. As Doodlebug pointed out, stall speed and Vmca increase with weight and so does the V2.

My understanding is that it depends!

Are you field length limited?

If so, if you are ASDA limited then V2 decreases with increasing weight. This is because you need more distance to stop.

If you are TORA/TODA limited then V2 increased as weight increases. This is because you need more time on 2 engines before one 'pops'.

If you are not FLL, then your V2 can stay the same as you increase weight until you do become FLL. Then refer to the stuff I said above.

I think.