The chip uses a bit unusual data protocol, but it's pretty simple. You send clock pulses to it, and it shifts out data. And apparently you've already figured that out. The main anomalies are that the amount of clock pulses you send determine what the chip does for it's next conversion, and you have to let it sleep a bit to make it predictable of when it does a conversion.
There is no way for the chip itself to convert it to a weight or force, because there is a wide range of load cells you can hook up to a chip like this. So the only solution is to calibrate it yourself and apply some math. The minimum would be to add / subtract a value to get to "zero", and then add some multiplication factor so your measured value is converted to the value of your calibration weight. You can also measure some extra weights, and then use them to check linearity.