On May 25, 1994, at 1215 central daylight time, a Piper PA-28- 181, N2331M, registered to Smith Center Kite Club, Inc., of Smith Center, Kansas, and operated by a private pilot, experienced an overrun on runway 35 (2,200' x 60' turf/gravel) at Browns Field, Weeping Water, Nebraska. The airplane sustained substantial damage. The pilot and one passenger reported no injuries. The personal 14 CFR Part 91 flight was operating in visual meteorological conditions. No flight plan was on file. The flight departed Freemont, Nebraska, at 1145. The pilot stated that he checked the windsock and it was favoring runway 35 but it was erratic. The pilot reported he was aware that the field was short so he made a conscientious effort to land slow and short. The pilot stated upon touch down he felt like he might have "picked up a surface tailwind." The airplane landed long, ran off the end of the runway, and went down an embankment. According to the pilot, the Fixed Based Operator stated "that the wind had been trying to find a direction all morning."