The fact that the carriage gets easier to move when the apron bolts are loosened suggests that the bed and/or carriage slide plates are not the problem. In addition to the procedure recommended by Ken, you also should try loosening up the bolts on the feed screw mounting block. Move the carriage as far to the right as you can, then tighten the bolts back up. This is a commonly-recommended adjustment, along with loosening/tightening the apron bolts. You want to do both adjustments with the carriage as far to the right as possible. Edit: Both adjustments should be done with the half-nuts engaged.
If neither of those work, take a closer look at the rack -- if it is thicker on the right side (or has some other problem on the right side), that could be your problem. I haven't tried it to see if it works, but it MAY be possible to turn the rack around and re-install it. If so, it would be a way to check the rack -- if it is bad, the carriage would become harder to move when it is moved toward the headstock. However, it's likely the rack is OK because I have never heard anyone complain about it in this context.
It also is possible that your lathe has a manufacturing defect that will prevent you from being able to completely resolve your problem with any of these approaches. I have heard stories where owners drilled out the feed screw mounting block holes, to provide more adjustment range. However, if your machine is new and it is determined to have a defect, I'd suggest contacting Grizzly before doing anything you can't undo.
