I don't think one should ask "What is your greatest weakness?" in such a context. It's not quite a job interview context, but it's close enough that it's likely to still be taken as "What's your best brag that you can phrase superficially as a weakness while not concealing that you're bragging?" and that's hardly a useful question. Sure, it can be a somewhat informative question in contexts where you can expect an honest answer rather than a boast, but even then you have to remember that you're asking "What do you think is your greatest weakness?" If you want to find out someone's actual greatest weakness you're better off asking those around them.