Although discussing it really does give everyone a learning curve, why not just check your manuals, or look at what happens in flight with respect to V1.
I don't know about larger aircraft, but go back to your turbo-prop days and you'll remember with take-off weight increases, V1 and VR respectively increase as well. For ex. a 1900C with a takeoff weight of 15,000 lbs will have speeds of 105, 112 and 125. 16,000 lbs is 107, 114, 125. The gap between V1 and Vr is not increased in this situation.
Funny thing is complex and rockie both bring up good points (and thank you both for sharing your theories). Braking a heavier airplane would require more runway theoretically, however V1 doesn't stand for "braking safety speed". It has to do with a failed engine recognition/decision speed. Think about it this way:
An aircraft is rumbling down a runway at a take-off weight of 100 tonnes vs it's average t/o weight of say 60 tonnes. If by complex's explanation, V1 is lowered for the aircraft because of it's heavier weight, then that means it has longer to accelerate to Vr on one engine, eating up more runway than if it had a higher V1 speed.
We can all agree heavier take-off weights means a higher Vr. So if the gap between V1 and Vr is increased for a heavier take-off weight, then the time and distance needed to accelerate on one engine between those two speeds would be far greater than the same example with a higher V1 (rather than a lower V1), thus shortening the gap between V1 and Vr, thus resulting in less time and distance to accelerate the aircraft on one engine to Vr and life off the ground. As for braking, the aircraft was designed to still be able to safely come to a stop with a higher V1 speed. The manufacturer would not publish a decision speed that the brakes wouldn't manage to accept for a given runway length/condition.
I hope I explained that well enough for anyone to understand. It made sense to me as I was typing it out
I'm by no means as experienced as many of you, but this is my way of understanding it. Please feel free to correct me if I'm wrong, I enjoy learning about the physics of flying.