A mostly theoretical rules question. Assume a Medium creature ("Grappler") has grappled another Medium creature ("Heavyweight"). For unimportant reasons, Heavyweight is very heavy- heavier than Grappler's carry capacity, but not so heavy as to exceed Grappler's push/drag/lift capacity.
The rules for moving a grappled opponent (PHB p.195) state:
When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you.
The rules for dragging a weight (PHB p.175) state
You can push, drag, or lift a weight in pounds up to twice your carrying capacity (or 30 times your Strength score). While pushing or dragging weight in excess of your carrying capacity, your speed drops to 5 feet.
If Grappler were to attempt to drag Heavyweight, in what order should these rules be adjudicated to determine how far Grappler could move?