I'd like to say something like "You do know grappa, don't you?", intending to mean "You have indeed heard something about (or tasted) grappa (an alcoholic beverage), haven't you?" Does this (the first quoted sentence) sound weird? Is there a better alternative?
Yes. 'Knowing' in that sense generally applies to people, languages, and facts. I'd say "Are you familiar with grappa?" or "Have you heard of grappa?". You could get away with "Do you know about grappa?"
I'd say it depends on the region. I know that it's common usage in certain areas of Australia. I do hear certain people phrasing their sentences this way.
Personally, it isn't weird or anything.
To others, perhaps this usage is unusual or singular. But I say, it all depends on where the audience and speaker comes from.
It's certainly not incorrect.
Generally speaking, "You do know" differs from "Do you know" in that it carries the implication that the speaker expects the answer to be yes. That is, if you say "You do know grappa, don't you?" you're saying "I believe that you know grappa, will you confirm this for me?" On the other hand, "Do you know grappa?" would be asking for a yes/no answer with no implied expectation.
"You do know"-style questions are similarly used in cases where the speaker wants to passively discredit the hearer in a condescending way. "You do know about [band I like], right?" can carry with it the sense that not knowing about the band is shameful or embarrassing.