In the days before automated stations, all of the equipment was housed in a Stevenson screen enclosure. Max Min thermometers had to be reset manually, and recording rain gauge and barometer paper had to be changed.
I suppose 9 AM was chosen to be shortly after arriving at work (for sites not manned 24/7), with time enough to ensure that the min temp recorded was really the min. 3 PM was late enough to record the daily max most days, but still with time enough before quitting time. Gotta remember to sling that old psychrometer around, too, and then look up the humidity.