I don't think WENO can be on all night because WNSR uses that tower and transmitter at night for 560.
Towers can be used for two, three and even four AM signals, day or night.
WNSR and WENO do not share transmitters. One is on 560 with its own transmitter and the other is on 760 with a different transmitter. You can't just move a transmitter from one frequency to another unless they were designed to be frequency agile, something American stations don't buy for medium wave operation (it was commonly used in the past for short wave where frequencies change at different times of the day).
As to sharing a tower, as fybush says, you need a combining and rejection network. Each station has circuitry that tunes it to the tower and additional circuitry to prevent the other station(s) from feeding back into its transmitter. Then, the combined signals are fed to the tower.
Look at the first photo at
David Gleason adds more stations in Ecuador and you will see me in front of a tuning unit that allowed one tower to be used by HCTM-570 and HCFV-805 in Ecuador in 1966. The technology today is pretty much the same except that we design with computers and not slide rules.
There is a bit more to this than my simple explanation such as the power handling abilities of combiners for stations of different output powers and the like, but the fact is simple that WENO and WNSR don't share a transmitter and both can run at any authorized time as long as the combiner/rejection networks are designed correctly.