bear, accept, undertake, just
當 centers on the idea of taking on a role or responsibility: bearing a burden, accepting a duty, or undertaking a task. The sense of 'just' or 'exactly' extends from being the one who is properly matched to the situation.
type of bronze Chinese coin first issued under Emperor Yuan of the Southern Liang dynasty worth the value of ten iron coins
ishigantō; stone tablet inscribed with the word "ishigantō" placed at crossroads, on stone walls etc. in southern Kyūshū and Okinawa to ward off evil spirits; orig. a Chinese custom
當 is the traditional form of 当. It combines 尚 (which may contribute a sound element) with 田 (field), suggesting a match or correspondence, perhaps originally related to a field being properly assigned or fitting.
The top part 尚 looks like a roof or covering, and the bottom 田 is a field. Imagine a farmer accepting the responsibility to bear the work of the field under the sun: that is undertaking the just task.
For トウ, picture a toe (トウ) stepping firmly onto the field, accepting the weight of the task: toe -> トウ, and the foot bears the burden justly.