Hi Magic
I had a few raised liver profile tests done years ago, Like yourself I was never a big drinker but I was overweight at that time and eating whatever I wanted , and mainly carbs. It was just after having my Son and I had had a very difficult time and had PND, anyway I digress. My Labs were bad. I ,like you went on the Atkins ,the weight flew off and I did increase my fat intake at that time and my Triglyceride levels (which were bad) came right down and my Liver labs came back in the within range, range.
So I have stuck with the low carb diet on and off since,and I'm not scared of fat, natural fats. Sometimes I'm lower sometimes higher carbs, depending on what my needs are at that time...but overall this lifestyle / diet has worked for me and my Liver is always within range now...
Also, it keeps my weight good, as you have mentioned. Go get a full check up done though as there are a number of reasons why Liver enzymes can be raised you need it thoroughly checking out, but in my experience following the low carb lifestyle has had nothing but a positive effect on my health....but that is just me, not saying it's the holy grail or anything :wink:
Let us know how you go on and the best of luck