It's not easy to troubleshoot over teh interweb
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If everything is clean, the same consistency of paint that sprays well through a paint cup should deliver properly through the gravity feed of the jar. If not, I'd say there must be a leak somewhere so that full suction is not achieved. The jar to airbrush attachment may not fit as tightly as the cup, it doesn't take much to screw up the air/paint flow. If it leaks even a small amount it will greatly affect paint flow. The jar/lid seal may not be good, the paint tube attachment to the elbow might not be good, the jar adapter to airbrush fit might be leaking.
How does the jar adaptor spray just water or thinner? How about in comparison to the paint cup? If the flow is interrupted from the jar using the thinners alone you definitely have a blockage or leak in the system.
I think replacing the jar adaptor is the wisest decision so far; keep us informed.