Anna's drinking out of habit for the same reason that the Salvatores drink so frequently: alcohol helps to curb the cravings and make people smell less appetizing than they actually are. She isn't sure why Elena's drinking, but after he conversation with Damon on the deck he and that guy who almost through him overboard destroyed, she can hazard a guess.

"And that's yet another thing that runs in the family."

She's talking about Jeremy casually hitting the booze, not whatever booze-y habits Katherine still has. Anna washed her hands of Katherine's bullshit some time ago.