I see what you are saying, and this could be true at the beginning of an addiction. For instance with an alcoholic, They may not know they have the “gene’, and think they just enjoy drinking. But if they begin to see the signs of having a problem early on, and do nothing to stop it or get help, it could be seen as being weak.
But there may be something else happening here. Maybe those with certain genes or mental illnesses continue because they are seeking a band-aid for their pain, and want a more immediate form of relief, and think they will stop tomorrow. then tomorrow becomes next week, and it snowballs on them. By the time this happens, the addiction itself has taken hold, and the brain/body connection with the substance takes over, changing the way the addict thinks.
I’ve gone through something similar with my ex. At first, he just liked to have a few beers on the weekend. Now, It takes a six pack just to be able to get out of bed. It’s both sad and pathetic at the same time. I think addictions are really a little of both weakness and illness to be quite honest.