This eventually changed to F-100 (for a 1,000-pound payload capacity), F-150 (for a 1,500-pound capacity) and F-250 (for a 2,500-pound capacity). In that case, you didn't have to remember that “F-3” meant “2,000 pounds” — you just looked at the truck's badge and you instantly had the payload capacity.
In 1948, Ford debuted the first official F-Series, aka the Ford Bonus-Built line. They ranged from the half-ton F-1, all the way up to the 3-ton F-8. According to Consumer Guide, because 'F' stands for 'Ford'.