and so's my wife

I'm tall, and so's my wife.

I looking for some way of understanding this kind of and so construction. Is it equivalent to the following?

I'm tall, and tall is my wife.

You could say, alternatively:

I'm tall, and my wife is tall.
I'm tall, and my wife is also.
I'm tall, and also my wife is. (maybe???)

So why is the 'is' moved before 'my wife" with the and so construction?

In the construction "I'm tall, and so's my wife," so is an anaphor; so refers back to tall. The construction is equivalent to, "I'm tall, and [tall] is my wife."

In linguistics, anaphora is the use of an expression the interpretation of which depends upon another expression in context (its antecedent or postcedent) ... The term anaphora denotes the act of referring, whereas the word that actually does the referring is sometimes called an anaphor (or cataphor).

Anaphora (endophora)

a. Susan dropped the plate. It shattered loudly. - The pronoun it is an anaphor; it points to the left toward its antecedent, the plate

b. The music stopped, and that upset everyone. - The demonstrative pronoun that is an anaphor; it points to the left toward its antecedent, The music stopped.

c. Fred was angry, and so was I. - The adverb so is an anaphor; it points to the left toward its antecedent, angry.

d. If Sam buys a new bike, I will do it as well. - The verb phrase do it is anaphor; it points to the left toward its antecedent, buys a new bike.

Wikipedia, anaphora

Thank you, Janus Bahs Jacquet