c. 1300, "so as to inspire reverence," from awful + -ly (2). Meaning "dreadfully, so as to strike one with awe" is recorded from late 14c. As a simple intensifier, "very, exceedingly," is attested from c. 1830.
1. Would you mind awfully waiting a bit, I'll be back right away.
2. The caramel looks awfully good.
3. These scissors are awfully heavy.
4. They're getting awfully weary of this silly war.