Think about what TSH is
: Thyroid Stimulating Hormone. If the thyroid is hypo-, i.e., NOT working as it should, is sluggish, etc, T3 and T4 will be LOW, metabolism is slowed and the TSH will be elevated. Why? It's the body's way of trying to, well, STIMULATE the THYROID.
Conversely, if one is HYPER-, that means the thyroid is working WAAAAAAAAAYYYYYY harder than it needs to, thus increasing metabolism (you'll lose weight). And, since the thyroid is working SOOOOOOOOO hard, it doesn't need to be stimulated, so the TSH (Thyroid Stimulating Hormone) number is LOW.
runningfool, my 9yo developed Hashimoto's, was on PTU for about 3 yr. Is euthyroid now. Hope you're doing well.