Dude,
Lightweight armor reduces the Mass of the armor, gives damage type resistances and reduces the amount of hull boost provided by the armor...
This stuff only works if you actually have bulkheads that are higher than lightweight armor. You know, Reinforced, Military Grade, Reactive Composite, Mirrored Surface..? That stuff.
If you have one of those bulkheads installed, Lightweight actually gives you MORE resistance than Heavy Duty. Lightweight also reduces your Mass, so that you can move faster and jump longer distances. The advantage of Heavy Duty is it even further increases your Hull Boost, which is effectively your ship health (armor).
That should clarify your mess.