Brief Answer:
This is a very tricky question.

Detailed Answer:
First, realize what a normal weight is, and that it varies with age.
http://www.cdc.gov/healthyweight/assessing/bmi/childrens_bmi/about_childrens_bmi.html
Then there is the question of proportion of fat, muscle, and water.
If someone is retaining water due to advanced liver disease, it is possible to have that improve after no longer injuring the liver with alcohol but it certainly is not guaranteed.
If it is due to the calories of the alcohol. and someone cuts out 2 drinks a day (upwards of 500 calories per day) then that would result in about 1 pound down per week (2 kg/month).
Cannot say in your particular case, but it is pretty clear how this would go if you know if your issue is water or fat.

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Brief Answer:
OH ! back up to normal

Detailed Answer:
ok.... several things on this....weight is both calories in and building up muscle.
First, alcohol can permanently break the pancreas... one of the chief digestive glands, and signs of this are diarrhea, diabetes, abdominal pain. If the pancreas is broken, it is going to be hard to both get calories in and to build back muscle. so, pessimistic if that is the case.
Then, there's if alcohol just meant the person didn't eat. This is easily fixed by not drinking. A regular multivitamin with thiamine and folic acid would be required to build back up from alcoholism which really lowers the levels of those vitamins. They are involved in most of metabolism, and they need to be present for normal utilization of food. BUT, if alcohol ONLY produced nutritional deficiencies. These get better with no alcohol and appropriate food and vitamin supplements. Still, muscle is really hard to build back up. Some weight back, really really hard at ages over 50 to build back muscle. weight lifting, and appropriate use of aspirin like drugs. BUT those have to be used ONLY under close medical supervision because their risk of causing serious bleeding is very very increased in heavy drinkers (and the susceptibility is not necessarily ever going to go away). And, frankly, the exercise needs supervision. IN normal over 70 yr olds there is some muscle build up. With the alcohol history it won't be as easy. Certainly feeling healthier and better muscle tone will occur RAPIDLY with food, vitamins and excercise (about 2 weeks); but the muscles only start to increase in a 20 yr old healthy person after more like 2 MONTHS! and an unhealthy 70 yr old will have a much much tougher time building up muscle. Fat, however, if the pancreas is present. If no other infections or illnesses are present. Should be able to be increased. If someone is really thin (under 15% body fat) then getting more fat is likely to be beneficial and quite possible.

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Brief Answer:
cannot say without an exam but

Detailed Answer:
presumably NOT with huge amounts of plain fluid in ankles or belly (which would be blown up like a baloon, tight, painful if fluid from alcohol).
Then...... a stable weight implies not much seriously going on, and likely to show improvment.
Furthermore, 182 pounds in someone 6 foot or less, is not that bad a weight... .close to ideal.
http://www.engineeringtoolbox.com/body-weight-versus-height-d_1551.html
on the other hand it is unlikely to be too heavy if you are over five foot six. So, if you feel you need more weight it isn't going to be bad in most everyone and without seriously odd things happening, it is likely to occur.
Frankly, main issue is long term sobriety and....
12 step programs (depending on what my son's math analysis shows!)

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