I have recently discovered this bug and must say that it's very annoying. As of now you cannot make a sky that is higher than 128 pixels and has no tiling effect. According to dpJudas this is something that's not easy to fix. Is that true? It's definitely frustrating to not be able to make this happen. It seems that this problem originated from the extension of the looking up pitch limit.
I have tried to simulate this with Heretic E1M1 with these results:
Capped when looking up roughly in an angle that is maximum in the vanilla game. You can see that the upper border is fading out. The bottom edge of the sky is untouched.

Capped when looking higher up. The sky begin to tile, fade out effect disappears and what is interesting, the bottom edge of the sky starts to fade out (sorry it's not entirely apparent on screenshot).

Normal mode. The sky is not fading out in any angle and the same applies for them bottom edge. Texture tiles.

Stretched mode. It behaves like normal mode. I assume that the code doesn't consider this necessary with 200 pixels high texture.

I am surprised that Graf accepted the looking limit removal without modifying the sky behavior. Now it's broken and only thing that player can do is setting "cl_oldfreelooklimit" to 1 via console. I wouldn't have a problem with that if the new extended limit wasn't a default setting.