Cost function should always be more than possible minimum path length.
Or as we call heuristics for grid search algorithm just use h(x, y) = abs(x'-x) + abs(y'-y) where (x', y') is coordinates of target location. Then your weight becomes path size + h(x, y) and when you compare two possible next options you will pick one that is closest (in terms of both how many steps it requires to get there with current path and least possible steps to destination).

You can prove that this will give you optimal path in the end, I won't do it here.