Well I don't know much about spinning factories(from cotton to yarn) nor dying process. But I know about knitting machine because we do some knitting.
Most tee are made from circular knitting machine, because they are fast.
People sell knitted fabric by the kilogram while weaved materials are sold by the yard.
The price of the fabric mainly depends on the yarn thickness because the thinner the yarn, the longer it will take to produce 1 kilogram of fabric. Also better yarn, needles and machines are needed to produce thin fabric.
Although the thicker yarn is cheaper per kilogram of fabric, it can be cheaper to produce t-shirt with thinner yarn material (to a certain degree), because you can get more yardage per kilogram. Once you get into super thin fabric, the price goes up significantly because most companies would use German made machines and very good quality yarn.
Sewing of the tees.
Tubes fabric: The width of the tee is already set from the diameter of the shirt. So we only sew the sleeves onto the shirt.
Non-tube fabric: We cut the material from a fabric made from large machines to the desired width. Then we sew the side of the shirt.
Tubes fabric cost more because each machines diameter is made for a particular size. You can't use a 23inch diameter machine to make a 16inch wide shirt, unless you want to cut it to the desire width. But that defeats the purpose of using tube fabric.
If you have the market, tubed shirt is cheaper to manufacture. If you don't then non-tube is the cheaper way to go.