To burn something just a little bit is to singe it. If you get too close to your backyard fire pit, you might singe your shirt sleeve.
When you singe your finger on a hot stove, it hurts, and when you singe your scarf on a campfire, you'll smell it starting to burn. The verb singe comes from the Old English root word sengan, "to burn lightly, or to burn the edges." One trick to the word singe is that when you add an ing, you need to be sure you keep the e — otherwise, instead of singeing, you'll be singing.