You can strap just about any mummy bag on a pack even if it is 5 or 6 lbs. That leaves open the question of quality over price. You can get a 30 deg mummy bag from walmart for $50-70. It will be heavy and won't last more than 7-10 years, but you can pack it. If you are concerned about weight and quality, you can get an entry level synthetic North Face/Marmot, etc, for around $100 down to 15 deg, like the marmot trestles 15. It will be around 4 lbs. You can go ultralight synthetic in the 15-20 deg range from the same manuf.s from $160-200 like the Cat's meow 20 on sale for 150 at just under 3 lbs. These are all mummy bags with some wiggle room, but not much.
For more room there is Big Agnes that are semi rectangular and wide mummies and Montbell spiral stretch bags in synthetic. Big Agnes saves weight by eliminating the insul on the bottom in leu of a pad, and Montbells spiral synthetic stretches for comfort. The BA mummy trim is decently weighted and well under 200, but some times the extra room means a harder bag to heat up. The Montbell 15 is back on the heavy side, 4lbs, but will stretch out to nearly the size of a semi rectangular bag for 210. Obviously bought at the right time, these can all be on sale or you can find some super high end bags on craigslist like western mountaineering. These are all down and bought new would be double or more than your price range. I would recommend going down to an rei and testing out different bag sizes to find the measurements you prefer. Then find the bag makers and models that fit and keep an eye out. Once a sale hits, make your move and you will be super happy. I have personally owned big agnes semi rec.s and montbell super stretch. The ba's semi rectangular were hard to heat up due to the extra room, so I was cold at much warmer temps than it was rated for. The montbell I have is super cozy, but their temp rating is about 5 deg optimistic for me.