I have a bit of a "swayed back" due to a spinal condition called spondylolisthesis, which is a vertebral slippage. Mine is a 50% slippage (classified as a Grade 2) at my L5/S1 vertebra, and it also causes me to walk a little "funny" (aka - waddle). A simple lumbar xray confirmed this for me, although I have also had 2 MRI's. My low back gets stiff and tight all the time, especially after bouts of inactivity such as sitting for more than an hour at a time...or sleeping overnight.

Perhaps seeing a reputable chiro who will do a simple xray (most will offer an xray with a new-patient consultation) can give you a better idea of what you might be dealing with.