At 5'8", and 200lbs, your body mass index is 30.4, which is considered obese. A BMI of 18.5 to 24.9 is considered to be a healthy range. Ideally, you should be 160lbs or less.
It sounds to me like your doctor was right in thinking that your elevated liver enzymes was due to your weight, as can be seen by the fact that they came down with weight loss. You can see by this that by only losing a small percentage of your body weight, you can make a big difference in your health.
Because your right upper quadrant (ie- the right/upper side of your abdomen) pain is worse with movement, there is a good chance that you have some kind of muscular strain. Right upper quadrant pain is also commonly due to gallbladder stones, so an ultrasound is probably a good idea. Fatty liver is often asymptomatic, but it can cause a dull ache in the area of your liver. Fatty liver can eventually cause serious damage to your liver, even liver failure over many years if you continue down the same road and continue to gain weight. Obviously an already damaged liver is not helped by alcohol consumption.
You really should have your blood work repeated and an ultrasound to see what your liver and gallbladder look like. If that's okay, muscular strain is a good possibility.
Beyond the shape your liver may be in, you really need to think about getting your health on track as far as lifestyle modification. Obesity can lead to many health problems other than fatty liver, and you are young, so this is the best time to make some changes that will serve you well for years to come. It's definitely not easy to make these changes, but if you do, the benefit you feel will be well worth it.
Good luck.
JMK MD