I did a little research, and I think I found a common link between frill size and horns and a potential explanation as to why Triceratops evolved this way. When comparing main predator of several ceratopsians (Styracosaurus, Chasmosasaurus, of course Triceratops) and their size, in respective order (Albertosaurus, Daspletosaurus, and Tyrannosaurus) one can see that the size of the frill for all but Triceratops acts as a shield for the sensitive nape of the ceratopsians neck. As a actual shield, in terms of functionality, it is weak but intimidating enough to prevent a predator to obliterate it with a charge. For Styracosaurus in particular, one can see the horns on top of it's frill are perfect for puncturing the neck of Albertosaurus in a situation where it goes for the back of the neck. The fact that these ceratopsians with large frills also have horizontal tails is interesting. Meaning it was unlikely they could use their hind legs to lift their upper torso off the ground.
I think Triceratops evolved considerable hind leg strength in order to rear up when fending of it's main predator, Tyrannosaurus Rex. When you look at Nasutoceratops, it's horns are formidable, but a Gorgosaurus could easily reach over and kill it with puncture of the jugular. The hind legs of Triceratops and Nasutoceratops are very similar, leading me to conclude they may of had similar strength as well as a similarly short tail. Since these two animals have similarly small frills and hanging tails, maybe they had small frills to reduce weight.