So I'm seeing if my parents might let me put a 4x4 fence post in yard at 8 foot tall to put a NEMA head on. Is it possible a 4x4 supports it, or maybe 6x6? It would just be a lightweight HPS NEMA head, nothing heavy, or special. And it might just be a temporary install. I might put my weather station on it too.

From what i've seen, a 4x4 should work, as i've seen a fair share of yardblasters mounted of 4x4 posts, so it should be sufficient for an HPS NEMA, but if you want to play it safe, then you can go for a 6x6 post. I would recommend using a pressure treated 4x4 or 6x6, especially if it's going to be partially buried.

See here.

That is a pressure treated 4x4 that is 8' tall. It is not in the ground, I used a mailbox anchor, and it rusted out and broke last winter. I haven't gotten around to setting it up this year. The fixture was not on the pole when it broke, fortunately.