Upvote:3
In theory, that's pretty borderline, your "personal item" is supposed to be an item (laptop, book, etc) and not a backpack.
In practice, though, I always travel with a rollaboard bag and a small backpack. Aside from the extreme LCC fringe (Ryanair, EasyJet, Tiger etc), I have never been questioned about this, and that includes a dozen or so flights on Asiana. I do make a point of keeping the backpack pretty flat, and in a pinch the rollaboard does extend enough to pack it in if needed.
The weight limit is for your "primary" carryon item only, and is intended to ensure that it's not going to break the baggage compartment or kill someone if it falls out.