A continuous weld, joining two materials, will shrink the metal .005 - .015, depending on the heat generated.
But, if you do as Jay recommends, welding small areas (.50") on opposite sides, it will not move enough, if any, to cause a problem. I'd recommend bending some 1/4" square stock to weld to on the opposite side.
If your not a welder, have it done at a competent shop.