The same is true of long hair supposedly (hair displays a record of illness). Does someone's attractiveness inherently change after a crew cut?

If you cant recognize the difference between weight and hair length as a reflection of health, I dont think we need to continue further

Now that's speed dating.

I’d venture that attractiveness does change after a haircut, with the degree of change being subjective. Does anyone truly think your hairstyle and length is not tied to your appearance?

Yes but that means different things in different contexts.

In some contexts a healthy weight is stocky with extra body fat that can carry a person through a cold winter or a famine.

In other contexts a healthy weight is leaner with less body fat to better handle a hot climate or chase down an animal.

Notice that I didn't say anything about what was healthy or attractive. Just that weight is a very valid measure of attractiveness. Though, it's simply universally valid that obesity nor very skinny are healthy, though the former is probably worse.