What size SEC is needed for 200A?

Since you are new to this site, the only advice that I can offer is to wait for a response from TK Russell. He is the go to guy for anything related to electrons going through wires or your body. Trust me, the wait is worth it. I look at all of his posts in an effort to learn new things. Good luck.

See page 3 of the product data sheet (http://www.cable.alcan.com/alcancable/en-US/Products/United+States/Stabiloy+Building+Wire+Products/STABILOY+Service+Entrance+Cable+Type+SE+Style+U.ht m) from a popular service entrance cable manufacturer, note SEU 2 wire with bare ground #2, is .919 inch,which is close to an inch.

Sounds close to what you have, only measuring the wire ,or even a knowledgeable person that can recognize the size wire, can be sure yours is #2, which is only good for 100 amps.

200 Amp requires at least #4/0 Aluminum wire per code, and it has been this way for my 30 years.

Smaller wire can only carry more amps when single conductor in free air, not when in a cable assembly.

Not saying the inspector is correct about his decision, but he should be able to accurate about the wire size, he sees many of this material in his job.

The incorrect size may have been overlooked or not inspected. Depending on how many people live there and the lifestyle, chances are you may have not or seldom went over 100 amps, but the chance is there, esp. nowadays with all the toys available.

If the utility installed it, which is done in many areas, they do have their own rules for the pole line, but not for homes. They must follow national and local electric codes.

Upgrading only this cable may cost between $100-$500, depending what market your in.