As long as you include them in your calories, you're fine. You can only gain weight by eating more than you burn. If you burn 2,000 calories a day, eat 2,000, but then eat 100 calories in grapes, then you'll eventually gain weight. But just eat them in moderation and you're good!
For some people eating a lot of grapes can cause weight gain. If a person is carbohydrate sensitive or has a degree of insulin resistance, too many grapes can cause weight gain even if they include them in their calorie allowance and do regular exercise. Many (but not all) overweight people have a degree of insulin resistance (often without being aware of it). Moreover, people who are obese are already significantly insulin resistant (with or without being aware of it).