Licensed PE here.
Commercial signage often uses Risk Category II unless it's remote. It rarely hurts to consider higher wind loads.
The wind loads via the ASCE Hazard Tool are a direct reflection of the wind maps in ASCE 7 Chapter 26.
When calculating wind loads, it's the velocity pressure times the signage area.
There are adjustment factors which often compute to around 1. Depending on the location, they can be higher or lower. I always compute a slightly more conservative value, meaning higher wind speeds, larger factors, etc.
For a 4ft x 8ft
sign (32 sqft) with a local engineered wind gust speed of ~110 mph, if the factors calculate to 1, the velocity pressure will be ~31 psf, which gives a force of ~992 lbs on the face of the
sign. With the top of the
sign at 7ft, the center of force is at 5 ft, giving a moment load of 4,960 lb-ft total or 2480 per post.
That would be relatively equivalent to 7ft of a uniform load of 88.6lb per ft.
The stress at the base is 2480*(half the thickness)/(bending moment of inertia). For a 4x4 (3.5x3.5actual), half the thickness is 1.75 in, and the inertia is 12.5 in^4, giving a stress of 347 psi.
Now, you can not use my numbers as PROOF, but yes, a 4x4 should be sufficient in this situation.
Default soils have a 1500 psf bearing capacity and a 100 lb lateral capacity.
At 4950 lb-ft, the concrete needs to counter that moment.
I could calculate that for you also, but I typically charge for that.