Can a 12 mcg increase in Levoxyl make a big difference in a hypothyroid person?

I had my thyroid removed when I was 18 due to hyperthyroidism, and I am now 42. Since the thyroidectomy, I have been on Synthroid or Levoxyl. Recently, I have experienced unexplainable weight gain and low energy. Last week, at my annual physical, my doctor learned that I am hypothyroid. My TSH is 4.62; T4 is .93; and T3 is 102. He raised my Levoxyl dosage from 125 mcg to 137 mcg. Will this make a profound difference? My gut feeling is that he should increase to an even higher dosage. What do you all think, based on your knowledge? Thank you!!