Weight-training question?

hopelessromantic26
So I've started weight-training in September. I've seen great results. I am currently 5'2 and 123 pounds, which I think is where I want to stay. My problem is I still have a layer of fat that I could turn into muscle, but the more I try, the more my muscles grow and yet the layer stays. I am starting to realize that my pants and shirts are getting loose around the middle area but tight around my upper arms and thighs. I follow my instructor-planned exercise routine to a T. What can I do to lean out those muscles or is this just a transitioning stage?

Currently I do a lot of weight lifting and 30 min on the exercise bike on random mode. I try to go almost everyday, but usually end up doing 4-5 nights a week.
Updates
+1 y
Just to make it clear, I am asking two questions


1) How do I get rid of the fat layer and


2) MOST importantly, how do I make it so my muscles do not bulge?
Weight-training question?
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