Deo, like all things there are lots of factors, but I also think the smaller point will penetrate better, everything else being equal. But, not for the same reason. Here's the physics, (borrowed from the background of the natal study).
A triangle point can be reduced to a pair of inclined planes. Forcing half a triangle point into something is like pushing a box up a ramp. So, comparing a 7/8" wide head to a 1 1/4" wide head both the same length is like laying a 8' ramp up to a 2' high truck bumper and pushing a box up. Then putting the same ramp up to the 3' truck bed and pushing the box up there. The additional height makes it harder. So the narrower head has less resistance and penetrates better (all else being equal). Now, for the same height, the longer the ramp, the easier the job. So, the little short 1" points, maybe an inch and a quarter long I've making lately are not going to penetrate as well as a 2" long 1" wide head and if I could make a 3" long, 1" wide head it would penetrate even better. Of course, the sharpness of the point matters a lot but if I made both points they're likely to be about the same.
There is also a component for the drag on the shaft and head due to thickness of the head, diameter of the shaft and the design of the point/shaft juncture. I don't believe the thickness of the head has nearly as much to do with that drag as how well the shaft is tapered into the point on the sides. So we need to be careful to taper the end of the shaft, particularly to make it smooth on the outside of the shaft into the point.
I personally don't think the weight of the point matters much except as it influences the width and length of the point and the thickness impacts what diameter of shaft the point will fit into.
Dang, was that verbose. Sorry.
George