Very interesting question and not much information out there on this.
Without tearing one or the other completely down, lets look at what can make that weight difference.
The heaviest components on an Inverter generator are the alternator assembly itself and the motor.
Let's give Honda and Yamaha the benefit of the doubt and assume they use they best materials available. Heavier wire for windings. More windings.... Heavier stronger Alternator casing.
Let's say the alternator on one of these weighs 10lbs more than cheaper priced comparable Inverter generators because of this.
Next is the motor. The single heaviest piece probably being the crankshaft, followed by the crankcase and then the cylinder and head assembly.
The crankshaft on these might be forged vs cast. That could account for another 5 - 10 lbs.(although i doubt any of these use a forged crankshaft).
The case could be a lighter weight casting compared to a heavier Honda / Yamaha casting. another 5 lbs maybe.
Pistons are usually cast aluminum, but cylinders can be steel (heavier) vs aluminum / steel sleeved. Rocker assemblies can be aluminum or steel.
It all adds up.
Next is the frame and plastics.
Maybe we can assume Honda and Yamaha put a bit more into each of these for quality and longevity sake accounting for another 5 lbs or so?
Another consideration "could" be that the Honda and Yamaha designs have been around longer and more recent generators have an advantage in design and lightweight materials for things such as the frame.
I don't know the exact answer and these are just some ideas. I "suspect" a good amount of this difference has to do with the weight of the power producing part of the generator itself.
These are just some thoughts since there are no other answers (yet).
Still, this is a good question and someone with more knowledge of the alternators themselves can provide more insight. I'll be watching this thread for replies.
To clarify - I'm not a Predator, but one of my Generators IS
HarborFreight Predator 3500 Inverter