If you want performance in the core, lighter balls don't give you much, I think, because the manufacturers expect the player is smaller in stature (woman, or kid, or older bowler) and the speed the ball is thrown (typically slower in lighter balls) needs to get a minimal amount of skid down the lane. A strong core in a 12 lb ball might get it hooking too much or too early when only thrown 10, 12, 14 mph.
Follow this link to specific info about the core in all the Twisted Fury balls down to 12lbs (look at the bottom of page 2 for examples of all the core shapes). The shape in 13 and 12 isn't bad.
The web link shows the cores in all the weights of the Twisted Fury. While the 14lb core is different than the 12lb version, the majority of effect is from the additional two pounds of ball weight impacting your ball speed, amount of rotation and consistency.
How you use a bowling ball provides most of the effect (you impart lift - rev rate, turn -axis tilt, rotation - axis rotation). I expect if you threw a 12lb Power Groove, 12 lb Avalanche, 12 lb Twisted Fury (and you'd find similar results from other manufacturers, I don't want to single out Brunswick), you would find a very similar reaction. So, is the expense for the higher end ball worth the money? When evaluating a lighter high end ball, look closely at the light products from the manufacturer and ask your bowling shop operator if another product can provide more benefits. I have found similar cores are available in significantly less expensive products.
Of course, the player will dictate what a ball can do. So, if you can't hit a golf ball, a $500 driver, won't help. If you can't throw a bowling ball, the most expensive one won't do much more than a basic one (no matter what the weight).