I do not understand why any illness should be described as a weakness. It is an illness. I have always worried about the way people talk about "fighting" cancer as it implies that dying means you did not fight hard enough and I am sure no one would want to say that.
If we accept that alcoholism is an illness, triggered in some people, not by moral weakness but by the way their body adapts and uses the substance, then we need medical intervention not moral opprobrium. I think that the idea of it being a "weakness" comes from it being seen as a mental rather than physical problem and, of course, we haven't understood mental illnesses very well either, have we.
I can see no way it is a weakness, anymore than my inability to process or produce enough thyroid hormone is a weakness. I can do things to help as can someone whose body reacts extremely to alcohol can but it is basically a medical problem and one we have yet to solve.
We have often blamed the patient for the illnesses for which we have not yet found a cure - hundreds of years ago we use to relate it to sin! You would think we had moved on from that by now.