First of all rule out the pregnancy
If pregnancy is not the cause for delay in periods,then overweight
or an under active thyroid
can cause delay in periods.
As far as increase in weight is concerned,you must get your TSH estimation done again.Of it is still high,you must get the dose increased by your doctor.
Other reason for increase in weight could be due to hyperinsulinemia
which might be due to polycystic ovary disease.PCOS in itself can cause delay in periods.
Lastly weight increase could be due to consumption of more calories and less exercises.
Consult your doctor and get examined and investigated to look for the medical cause of weight gain and delay of periods.
Reduce your calorie intake and do regular aerobic exercises for at least 40 minutes a day.