Is my gramps short and overweight because he is old or because of how he lived his life?

Both. I obviously don't know your gramps so can only address your excellent question generally. Dietary indiscretion is the main cause of obesity and many elderly people remain lean and fit, but it's also true that metabolism slows with age. For instance you may burn 3500 calories a day when you're 18 but maybe only 2000 when you're 70.