Wood deck post off centered

You wouldn't calculate the sonotube for axial only anymore. It would now be axial + bending moment, where the bending moment is eccentricity (say 2") times axial force. If it's reinforced sonotube (though I doubt it for such small diameter), it should still work.

Technically, the bearing pressure distribution will also change. Sonotubes work with skin friction and bearing pressure together (though I only design them for bearing pressure). You could use the skin friction to help with increased bearing pressure at one side. Though I'll be honest, I have no idea how to calculate this kind of thing. I'd look into manuals for eccentrically loaded drilled piers. If the stress in the sonotube is well below combined flexural/axial capacity, I'd use that as a sign post to determine whether complicated bearing pressure calculations are needed. With the rate I charge clients, at the point that I see that there's a problem, we're looking at reinforcement or post correction rather than doing like 4 hours of calculations. It is just a tiny sonotube after all.

I'd say let the numbers lead your decision about what to do. If it's failing by a small amount, you can work on optimizing the loading of the post (things like live load reduction). If it's off by a lot, you might have to start looking at reinforcing the sonotube or correcting the offset in the post, or adding another sonotube and post somewhere else to reduce the loading.

Deck foundations are quite prone to settlement and failure in my experience. I don't know why; maybe it's because they're so exposed to wind and rain. So I wouldn't just brush this off.

I'm going to disagree with MSL on skin friction... the concrete shrinks and the cardboard roots away leaving a questionable interface with soil. Maybe there are tests to prove me wrong?

But yeah - it's eccentric. So lame or not, that's what you have to check.

Unlikely to cause a problem with the concrete, but might be a soil bearing issue

Depending on the treatment, it's not normally good to have wood directly on concrete... What sort of load? The load appears to be out of the kern; can the concrete take the stress in plain flexural tension?... about 8 x sqrt(f'c) or about 0.1 x f'c.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

How deep is the footing?

If it’s reasonably deep and upper soil is sound then the passive resistance of the soil can rectify any imbalance.

Thank you everyone for the replies.
I'm not sure how deep the footing is. The contractor is arguing it's 4 feet deep.

Alan_CA, what is the situation here? I am sure you aren't just being asked to opine on this. If that were the case, I would just state my opinion that the load being significantly off-center results in eccentricity which is may cause the the footing to settle unevenly over time and tilt to one side. Is this possibly a deck that was built without a permit or AHJ inspections, and now you are being asked to verify and sign-off that it is code compliant?

I like Tomfh's suggestion. If the footing has decent embedment into decent soil, you could try using passive pressure to balance.