Are babies cute because they have big eyes, or are big eyes cute because babies have them?
Mods: Feel free to move this to GD if appropriate. 
Given that a big round head, squealy high pitched sounds, short limbs and several other aspects associated with young offspring are also cute, I think it comes from the fact that young offspring have them. Or young offpsring just happen to coincidentally have pretty much all the cute markers.
Puppies are the cutest, followed closely by lion cubs.
Baby chicks are cuter than eggs. Hope that helps.
I read once (in some Time/Life book on animal behavior if you need a cite) that warm blooded animals are almost all wired to react to these “baby animal” markers. I suppose the suggestion there is that I’d see a baby cat or duck or otter and feel some parenting instinct but I’d think a predator would just see them as markers for “easy meal”.
Parents who see their offspring as attractive are more likely to take good care of them and thus have more living descendants. Simple as that.
Mariah Carey was really cute when she was in her big, doe-eye with long hair period, circa Music Box.
Perhaps we should differentiate between different types of cute. There is “I’d like to fuck him/her” cute and there is “kitten/kawai cute” and, while they may intersect to some degree, they’re still rather different.
If, for most people, they intersect at all it is that kitten/kawai cute and fuck him/her cute are related to youth. Mariah Carey in that picture is 24 and could pass for much younger because of her skin and facial features/shape.
The intersection may be related to teenage girl-targeted pedophilia; teenage girls go from kitten cute (creating feelings of protection because of their vulnerability) to fucking cute (because of the many years of fertility ahead) and I guess the two can get mixed up.
May I speak honestly? Thanks.
Compared to most mammal babies, human babies are near the bottom of the cute scale. And yes, I have a child.
Once you take away the emotional component, babies are mostly blobs of skin that drool, spit up, cry a lot, and poop.