How common is 'Sweet as' in the rest of the world?
Solution 1:
Being from the United States (the Midwest), I've never heard the phrase. I doubt that I would've been able to discern its meaning out of context. That said, we use quite a few idioms that begin with those words: "sweet as pie," "...honey," "...sugar," etc. Basically, it would only be used when followed by a sweet object in order to call something else "sweet" by comparison. We sure do love our similes!
For what it's worth, in the context you mention, common responses from these parts of 'Murica would probably be "Oh, you're fine," "Don't worry about it," or if you want to get really slangy, perhaps a "No prob." :)