Thank you for the additional information.
It is unlikely that going off of BC pills will cause weight loss. For most women, being on BC pills cause weight gain ( due to retention of fluid by the high level of progesterone
) and going off the pills will eight cause no weight issues or cause weight loss.
Yes, A LH level higher than FSH at day3 does suggest PCOD. Normal the ratio of FSH:LH should be 1:1. In your case, although the LH is high , it is not significantly high. Please repeat the test after another month to see if the ratios has stabilized. If it has not , or if the LH level has increased further, please ask your Obgyn to evaluate you for PCOS.
In your case, it is possible that the level of TSH has increased and you need to adjust the dose of Levothyroxine. Since TSH is secreted by the same area of the pituitary gland that secretes FSH and LH, going off the BC pills can cause some amount of hormonal imbalance which can also affect the TSH level. This effect is usually temporary and stabilizes in about 3 months. But you do need to get your TSH level checked.
A repeat blood sugar level should also be done.
Please consult your doctor for these tests.
I hope this helps.