The weight and sleep issue brings up the possibility of sleep apnea where the airway narrows during sleep and oxygen levels dip then you briefly awaken and start the process over -- ask your primary about this.
The cytomel/synthroid combo is not unusualy. It is worth a try to see if you feel better. Most common cytomel dose is 5mcg 2x/day in addition to the synthroid -- keeping the TSH around 0.5-1.5.
I thought you might find it interesting that I belong to a large group of thyroid patients, and those that were once on Synthroid and Cytomel, and then switched to Armour, which is natural dessicated thyroid, said they noticed MUCH better results. I personally never had Cytomel added to my T4 meds, but when I switched to Armour, which gives you exactly what your own thyroid gives you, the difference was stunning. Also, those of us who are having such great success have docs that does us by symptom-elimination first and foremost, not the TSH. We also get our free T3 towards the top of the range, and there is where our hypo symptoms stop, such as weight gain, achiness, hair loss, etc. Also by the way, a LOT of folks seem to have sluggish adrenals, which means not enough cortisol is being made to distribute the thyroid hormones from the blood to the cells. So these folks are getting their adrenals checked with a 24 hour saliva adrenal test. They say a one-time blood test doesn't do the job.