Yes, it's possible to gain weight by eating too much fruit, but it's very hard to actually eat that much fruit. You'd have to be a fruit addict or something. The average person requires 2000-2500 calories a day. If most pieces of fruit, like an apple, contain about 60 calories, you'd have to eat 50 apples, or similar fruits a day. Does anyone have 50 servings of fruit a day? Of course, if you're already getting all the calories you need from the other food you eat, then extra fruit, or anything, will take you over your needs.
Plus, the carbohydrate from fruit is fructose, a very starchy sugar which gets released into the bloodstream slower than table sugar, so it's more likely to be used as energy than it is to be stored. Any extra gets stored as glycogen--body starch--which is readily converted to glucose to satisfy energy needs.