Addiction can be a tough thing to RP as the problem is addictions are not just limited to the physical impairment but the social impacts too. Most alcoholics, especially one in the middle but not true 'burnout fall over drunk' like I see in the ED all the time are likely not going to even notice an 'average' quantity of substance. They'll more likely notice an absence of it. And if the addiction gets worse, that'll even be more true as there will come a point where the character HAS to have booze in their system or they starting to have physical issues because their body can't handle being sober. (Withdrawal is an ugly, ugly thing)
Social modifiers due to just a surliness or the Johnson smelling the hard booze on their breath at a meeting could also be a mechanical disadvantage. Even if the character isn't impaired from the two drinks, the appearance of being a hard core drinker could be negatively impactful.
Also could start to eat into the character's time and activities, which depending on how the character operates might impact contacts. Jim has stopped being available to go clubbing/AR VIdeo game night/driving/scouting the city for upcoming run/etc because he's making liquor runs or down at the bar instead.
Might also hit it as a life style cost. If character has a Low lifestyle but at that addiction level might need the medium lifestyle aspects that covers drinking (if you use the advanced life style rules) or just take on a 5-10% cost increase due to volume, especially if the character is a 'quality' drinker and not just downing jet fuel.