Does the height of something effect the gravity?

So, in physics we're building a bridge... made of toothpicks and Elmer's glue. We are going to test the strength of each of them by putting weights on them. I was wondering... if the bridge is slightly elevated from the ground and then has weights put on it, will it hold up better than when the bridge is elevated to a higher point and then has weights added to it? Why or why not?