[BipolarBob]

and it is foolish to claim He would use the same word twice, in the same sentence, to mean different things.

Actually that is not true. Eastern dialects and Aramaic idioms would employ such usages to make a point or a pun. In this case Jesus was contrasting the smaller shakier rock of Peter with Himself - The Rock. The Apostles and anyone else at that era would have understood and enjoyed construction of that sentence.

[Mrs. Don-o]

It's just that petros and petra did not mean "small" vs "big." Not in Koine Greek.

In Attic Greek, maybe: but that's 500 years beside the point.

As for Jesus' next phrase: He would have said "upon Me" if He meant "upon Me." The point here is that He was talking about "THIS" Rock, which would apply to the man he had just named "Rock."

Jesus (God) is the Rock in the ultimate sense; so the sense of this commission of Peter is that Peter is to have a share in Jesus' ministry.

Whch I hope we may all have. I pray for it every day.