I don't know about the relation to building material sizes, but here's a brief history of Ford's pickup boxes as gleaned form a very well researched and written history of Ford trucks ("Ford Trucks Since 1905" by James K. Wagner):
1925 - first Ford pickup box (an optional body for the Runabout car chassis), 56" long.
1931 - new pickup box, 59.4" long.
1938 - new 1/2 ton pickup box, 77.7" long (not quite 6.5'!).
- new 1 ton express (pickup) box, 96" long x 54" wide.
1939 - new 3/4 ton chassis gets the 96" box.
1948 - completely new F-series chasses, but all with carryover pickup/express boxes with restyled fenders to match the new cabs. F-1 has the 6.5' (not quite!) box, F-2 and F-3 get the 8 footer.
1951 - pickup boxes are redesigned, but still have the 1948 fenders.
1953 - completely new series of trucks, including the pickup/express bodies:
-F100 (1/2 ton) has 6.5' box,
-F250 (3/4 ton) has 8 footer, and
-F350 (1 ton) has 9 footer.
1956 - in response to Chevrolet 3200 series 1/2 ton long wheelbase, the F100 is available with either the 6.5' or the 8' box.
1957 - full-width (Styleside) or regular width (Flareside) bodies available in all 3 lengths.
1973 - F350 gets 8' box, the 9 footer is now history.