Prior to taking off on the aerial application flight, the pilot loaded applicant and fuel which, as reported by the pilot, put the airplane slightly over its maximum gross weight. In addition, he checked the automated report for the nearest airplane weather facility, which reported wind from the north at 4 knots. The pilot departed the private strip, a 2,600 foot-long turf and asphalt runway, to the south toward a river. While on the takeoff roll, with a tailwind, the pilot rotated the airplane for takeoff at the usual rotation point. The airplane climbed to about 3 feet then settled back to the runway. With a quarter of the runway remaining, the pilot continued the takeoff, increased flaps, and verified that the throttle and propeller controls were full forward. The pilot again rotated the airplane and was able to climb about 4 feet when the airplane again settled back to the ground. The pilot then dumped the application load and tried to maintain control of the airplane. The airplane continued a short distance to the opposite river bank, impacted terrain, and slid on its belly. The pilot reported that during the preflight checks the airplane had adequate oil and the fuel was sumped of any water. In addition, the pilot reported normal engine instrumentation prior to the takeoff roll.