Like most things in the regulatory environment, one needs to put lines in the sand. There need not necessarily be a sound, theoretical basis for such boundaries .. and, on some occasions, a good old finger in the wind engineering WAG is used in lieu ....
(a) according to a tale which I heard about 15 years ago during a training course .. the source was one of the instructors .. and a quite elderly chap at that time ... This chap was a long ago FAA engineer, who was around as a young chap in those ancient times. According to his tale, an early military demonstration of, as I recall, a Curtis machine, involved flying in and out of an Army parade ground. The particular parade ground was surrounded by a line of trees whose height was in the order of 50ft. The early CAB folk adopted that as being as good as any figure, on the basis that the need was to have some provision for notional obstacles to be addressed during the takeoff and landing. This then became the standard for light aircraft.
(b) at some much later stage, the heavies moved to 35ft screen. Unfortunately, I have never seen any historical discussion on the specific reasoning. However, one could presume that this had some basis in the more rigorous takeoff treatment accorded to this class of aircraft. The 50ft landing screen remained.
(c) at a yet later stage, as the Industry moved to account for contamination on the runway surface, a compromise for heavies was reached in adopting a 15ft screen for takeoff for wet runways.
Perhaps others can provide additional tales relating to the 35ft history ?