Terrel Miedaner's story The Soul of the Mark III Beast (1977) republished in 'The Mind's I' describes this situation exactly.

https://www.amazon.com/Minds-Fantasies-Reflections-Self-Soul...

Have a look at the "The mind's I" [1]. It is a collection of essays and other short texts on consciousness, self, AI and strange loops with added commentary by Hofstadter and Dennett.

[1]: http://www.amazon.com/Minds-Fantasies-Reflections-Self-Soul/...

An interesting collection of essays and short stories that investigate concepts related to your observation is http://www.amazon.com/The-Minds-Fantasies-Reflections-Self/d..., which I'm almost finished with. It has a lot of thought-provoking arguments. Edited by Douglas Hofstadter and Daniel Dennet.

Weird compared to what? I have no experience being anything other than a living, breathing human. Thomas Nagle wrote up the classic "qualia" argument you're making as "What is it like to be a Bat?" (here: http://www.clarku.edu/students/philosophyclub/docs/nagel.pdf..., it seems persuasive: that there is a certain subjective quality to consciousness & conscious experience— it must feel like something to be a bat, or a person, or whatever? Hofstadter's and Dennett's book, The Mind's I (http://www.amazon.com/Minds-Fantasies-Reflections-Self-Soul/...) is an interesting introduction to this kind of stuff, the authors have a lot of fun @ qualia's expense.