This Spring I noticed that when I ride with medium weight tights over my shorts,
my butt feels much better. These are unpadded tights, but with the extra lycra under
my shorts it seems to make a difference. I can go much further before my butt gets
sore.

Anyone else notice this effect?

So I am wondering if shorts with thicker padding would help. I'm on the thin side, 5'9", 145 lbs, riding a Koobi Silver saddle and I wear Boure Pro shorts, which have thin padding.

That's probably an effect of friction, or the lack thereof. The tights stick to the saddle a little bit, they slide against your shorts/bibs, the shorts/bibs stick to your butt. With out the tights your shorts/bibs stick to the saddle a bit and the sliding hapens between the butt and shorts/bibs. This is why hikers (a group I once belonged to, way back when) wear liner socks, no matter how hot, it keeps the blisters away.