What wiggles on the faucet? Explain "it" please

The faucet itself wiggles. The mounting assembly is tight, that is to say that there doesn't seem to be any give in the faucet where it is mounted on the sink (undermount SS on granite countertop). But the upper portion of the faucet (which is not named on the parts list) wiggles in the part that is labelled as the base.

The plumber did not install the stabilization plate; he insists that that has no bearing on this particular problem.

Here is a link that might be useful: Parts list

Ah - I think the part is called the spout.

I have this same model in different versions and all are tight, I would suggest you call Delta Customer Support. Delta has a lifetime warranty on their Faucets. The Customer Support information is:
If you need immediate assistance, call the Delta Help Line at 1 800 345 DELTA (3358). The Delta Help Line is available between 7 a.m. and 9 p.m. (CST), Monday through Saturday