The word "him" refers to anyone who is suffering and who waits for Yahweh. Here "offer his cheek" represents allowing someone to strike his cheek. Alternate translation: "Let him allow people to hit him on the face" (See: [[rc://en/ta/man/translate/figs-metaphor]])
The author speaks of a person as if he were a container and reproach were a liquid. Being filled with reproach represents being reproached much. The implication is that he should be patient when this happens. Alternate translation: "let him be insulted much" or "let him be patient when people reproach him" (See: [[rc://en/ta/man/translate/figs-metaphor]])