From be- + weigh. Compare Dutch bewegen (“to move”) and German bewegen.
beweigh (third-person singular simple present beweighs, present participle beweighing, simple past and past participle beweighed)
- (transitive) To determine the weight of; weigh; consider.
1809, Sir Ralph Sadler, The state papers and letters of Sir Ralph Sadler, knight-banneret: Volume 1:
But the governour is sufficiently warned thereof by the common bruit of the people; and also, I shall not fail, on your lordships behalf, to advise him to beweigh the same, in such sort as ye require me by your said letters.