In Korean culture it’s polite to give things to people with 2 hands, or with the other hand supporting your arm. It’s especially important to do that with someone older than you or if they are in a higher position.
Being married, we don’t need to always give things with 2 hands (though some people who have a more formal marriage may still always do it) so it was funny that Hugh did it by reflex when he was concentrating too much on something else but still didn’t actually look at me.
Within a marriage you can also do it on purpose to show respect or care but is not necessary all the time. Also because I’m not Korean and our marriage is a cross cultural marriage, we are changing between 2 different cultures constantly.