I have been doing some weapon throwing with barbarian, and unless I am missing something, throwing a weapon designed to be thrown rolls weapon attack damage (in my case 1d6+ modifiers) PLUS old weight based damage. I have been doing on average more damage with my handaxes then a battleaxe

Weapons with the thrown properties make the weapon damages + modifiers.
The other weapons makes 1 damage.
"Improvised weapons" seems to have their own damage range depending the items.