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.
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.
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