I've been taking thyroid medication for about 30 years now, but it was because of adenomas on the thyroid so it was removed (actually one lobe was removed when I was 12, the second when I was 23). I started out at over twice the dosage I'm taking now so whatever little piece of thyroid is left is doing its job.
If your doctor isn't worried about the low T3 or T4 number, then don't worry unless you experience some symptoms. Hopefully your doctor discussed those with you. People with overactive thyroids do lose weight rapidly, but usually it's accompanied by some very noticeable symptoms like rapid heartbeat and excessive sweating. The best thing to do is get it checked regularly, which is sounds like you're doing.