Looks like a fairly new expansion tank, doubt that would be the problem. But it's a quick 5 minute check and you can rule it out.
Turn off incoming water, open couple faucets to relieve pressure and check it with a tire gauge. Should match your incoming water pressure usually 55-60 psi or so. If not, add air to the appropriate psi. If nothing but water comes out, replace it. Just a suggestion.
If that checks out good, I agree, then it's probably the check valve.