When you tweak something, you pinch it or twist it. You may have a doting aunt who thinks you're still two years old and can't resist tweaking your nose every time she sees you.
Tweak also means to adjust or fine-tune. When you finish writing a paper, it's a good idea to go back through one last time, to tweak it and make sure it's absolutely perfect. So when you tweak something or give something a tweak, you're making little adjustments, you’re not rewriting your paper or tossing it out and starting all over again.