Everyone is different and people need different amounts of levothryoxine. There isn't an upper limit as such. Levothyroxine can also vary in strength which may affect how much a person needs to take. I have been on 250mcgs at one point only to find out that the levothyroxine was faulty and that was why I needed so much! Most people take between 100 and 200mcgs and 125 to 200mcg seems quite a normal dose if you read people's accounts on this forum.
TSH 4.70 (0.27 - 4.20) TSH is over range. The top of the lab range here is 4.20 and your result is 4.70, showing clearly you do not have enough thyroid hormone. Most people don't feel well until TSH is 1 or a little lower.
FT3 3.2 (3.1 - 6.8) FT3 is very low in range indicating that you do not have enough FT4 for your body to utilise and turn into T3. Your body needs T3 to function effectively. FT3 is best in the top third of the range.
FT4 14.8 (12 - 22) Your FT4 is low in range and is best in the top third of the range.
You would benefit from a dose increase of 25mcg and then retest in 6 weeks time and adjust dose and retest and so on until your TSH reaches 1 or a little lower.
Your TPO antibodies are elevated showing that you have autoimmune thyroid disease otherwise known as Hashimotos.
It's possible you have absorption problems as many people with Hashimotos do. It's worth getting your GP to test vitamin levels. B12, folate, ferritin and vitamin D. All can be low in people witth thyroid disease and prevent efficient conversion of T4 to T3.
If your Endo is concerned about increasing your dose of levvothyroxine he/she would do well to look into any possible absorbtion issues rather than refusing to increase your dose of levothyroxine. Do you have symptoms and if so, what kind?
Just one more thing to check, are you taking your levothyroxine with a full glass of water on an empty stomach and then waiting one hour before eating or drinking anything except for water and are you taking any other medicines at least 4 hours after taking thyroid meds?