Gatsby has several needs for control. His job seems to be one that requires he be ready to receive a call at all hours of the day. As he has been on this journey to entice Daisy back to him, he didn't need to get caught up in any relational traps with other women. He regularly had his house full of people who did drink quite excessively and his alertness was probably called for in more than one occasion. Take for example the night Owl Eyes drove his car into the ditch outside the house.
Daisy doesn't drink much either. This is important because we find that the teenage infatuation he has for her has not stopped. Perhaps he uses this just in case he might run into her. He wanted to be perfect for that moment.
This is not made very clear in Chapter 6. This chapter is talking about how Gatsby met Dan Cody and what impacts Cody had on Gatsby's life. One of the impacts that Cody had was that he, indirectly, made Gatsby not want to drink much. So I guess the answer would be that Gatsby doesn't want to drink too much because he doesn't want to be like Cody was when he drank.
The book says that Gatsby had had to be Cody's "jailer" at times. That implies that Cody got out of control when he was drunk. Gatsby's character does not seem to be one that would enjoy being out of control and I think this is why he hardly drank.
Gatsby is a man of many secrets. He has carefully built a life that is based on pretensions and built on implied illicit dealings. As such, he must always maintain control. He is an outside observer at his own events even, carefully watching not only the crowd but also his own back. Look around him at the actions of other characters when they drink (such as Myrtle and Tom) and notice that in doing this they speak their minds which leads to arguments. That, or they end up killing someone else (Daisy). This was a common theme of the 1920s and a common theme of prohibition, but it is also a common theme in the illegal drug world today. Drug dealers, the ones who survive and are not arrested or killed, are rarely users of their own product for they know that the only way to stay safe is to stay clean and clear-headed. It is implied that there was a time when Gatsby himself was a drinker, and part of Dan Cody's advice to him seems to have been to teach him ways to stay in control. Also, while this takes us to the end, when we see what Gatsby's father shares from his old school book -the lists Gatsby had made as a plan to become a success, we can see that he was always willing to do what it took to get him to the top. If not drinking was a part of that plan, then he would not drink.
Another possible reason for Gatsby's not wishing to drink too much is that since liquor is known for loosening the tongue, Jay Gatsby may worry that his fabrications about himself may inadvertently come out. For, even when he makes conscious efforts in his tales about himself, he sometimes slips and tells the truth. For example, he professes to have traveled many places, yet he thinks San Francisco is in the Midwest.
Playing the role of the Oxford man is no easy task for Jay Gatsby; if he drinks, the challenge will be even greater. Besides this problem, Jay Gatsby perceives himself as the pursurer of "the grail," and "the dream." As such, he is loyal to the dream and acts politely in order to ingratiate himself with the wealthy.