讓 hands over leave to act, with a verb after the person; 給 hands over a thing, with an object after the person. 讓我看 = let me look; 給我看 hands me something to look at.
他讓書我看。 → 他讓我看書。 (person right after 讓, then the verb phrase)
請讓坐這裡。 → 請讓我坐這裡。 (name the person given leave)
他幫我休息一下。(when you mean: let me) → 他讓我休息一下。
English 'let me sit' puts the bare verb after 'me'; learners drop the person or slip an object word in, where 讓 needs the person first and the full verb phrase after.