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It really depends on how you define weight. The classical layman's context is "force normal to ground" than buoyancy matters, if you use rigorous engineering context of force exerted by gravity than you wouldn't include the buoyancy.
A bit of a semantics thing. I have designed instruments that measure weight on bouyant systems (drill collars) for 20 years, and the one thing that is consistent is people mean different things when they say weight. It is better to more precisely define what one means by weight than have a semantic argument over what the term means in isolation.
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