If you're more than willing to do something, you'll do it gladly, with enthusiasm. Most people will gladly accept free passes to an amusement park.
You can offer something gladly: "I'll gladly give you a ride to the movies tonight." And you can also receive something gladly, with gratitude: "I gladly accept this award on behalf of all the fire jugglers that came before me!" Gladly comes from glad and its root, ghel-, which means "to shine," as in shining with happiness or being radiant with joy.