Hi,
you will need tenzo sensor the popular name is the "load cells"
_______ _____ _______
o.........o.o.^. o.o......... o
.....A..........LC........B.....
this is your conveyor, actually this is the standard configuration. The middle part of the conveyor measuring the weight. The load cell measure force over this middle part. When the object is transfered from A to LC you must stop the conveyor and make measurement. Actually you no have a need to stop the conveyor , but in this case you must be sure that will reject any innertion force that can insert error. You must have some manipulator to remove the object, or just stop the conveyor if the weight is not correct.
The directly use of PC for this is not a good idea, you must have the controller, this controller will drive your motor, for this no have a need of using the stepper motor, every type of motor is suitable, but more importand controller will make the measurement.