Praise be to Allah.
Firstly, it is permissible to buy chicken by weight. This is the basic principle and we do not know of any evidence (daleel) to the contrary.
Secondly, it was reported that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Whatever intoxicates in large quantities, a small amount of it is haraam.” (Narrated by Ahmad in al-Musnad, 2/91, 167, 179; 3/343). If the vinegar would cause intoxication in large amounts, then a little of it is haraam, and it comes under the same ruling as wine. If a large amount of it does not cause intoxication, then there is no reason not to sell it, buy it or drink it.