The sweater will definitely be bigger, but you'll need to do some math to figure out how much.
Knit a swatch with your yarn on the 13's and see how many stitches per inch you get. Then use that figure and divide it into the number of stitches in the sweater--back and two sides, totaled. That will give you an idea of how large the sweater will be.
For example, if you get 3 stitches per inch on the larger needles, and there are a total of 150 stitches in the sweater, then the sweater will be 50 inches around.