It is important that you keep these little weep holes free from debris, and certainly don't block them with caulking and paint. It could make the difference of you sill rotting out, your drywall being damaged, your insulation saturated, your carpet getting wet, or your hardwood floor being ruined.
There are times after a driving rain against the window that the weep holes may not be able to handle all of the moisture and your sill and floor may be wet. If this happens you may want to test your window using a garden hose. Sometimes a window just has to be replaced. Don't worry, windows aren't that expensive. But do yourself a favor and hire a professional who will replace your window and exterior trims, caulk them, and paint them. It's worth the extra cash you will put out.