High index lenses won't change the appearance of your eyes, that's due to the power of the lenses, which you can't change. High index lenses will be slightly thinner. Compared to very low index materials that we used to use, high Lenses are thinner.Aspheric lenses may not magnify your lenses as much. The magnification formula includes thickness so at least in theory, thinner lenses magnify less.
Actually, the eyes bigger/smaller effect from glasses is dependent on the power of the lens, not the refractive index, size, shape etc, so, regardless of what index lens you get, your eyes will look bigger by the same amount. Of course, the higher index lens will typically be thinner & lighter so might still be desirable. There might be some kind of make-up trick to make your eyes look smaller though.
Thick lens make wears' eyes look smaller as well as the high index lenses. However, index lenses are much thinner than normal eyeglasses materials, but it can also case slight the same. So, actually, it depends on your prescription. Hope this helpful.