You're talking about 40 - 60 pounds of weight, which is pretty insignificant in a 4000 pound vehicle. But if you really want an idea of what it would feel like, just note the difference in handling between a half-tank and a full-tank of gas. About the same weight difference (low and in rear) without really having to engineer anything.

If you'd like to feel better about the stock location of the battery, keep in mind it's where it is to offset the weight and location of the driver just a bit.