What's the meaning of "if for no other reason"?
The whole sentence is "But now you're here, and a week after your birth, I still sit for minutes watching your chest rise and fall--if for no other reason than it's more interesting than the other reality shows on TV". I don't know how to use "if " here.

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This statement means that there could be other reasons, but at least one reason is "it's more interesting than the other reality shows on TV".
If you did not use "if" here, then the statement would be very different.  It would instead mean "this is the only reason".  
So, if you say "For no other reason," then you are eliminating all other possible reasons.  When you add "if", you are specifically saying that all other possible reasons are still valid, too.

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just because of that perfectly valid reason

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unless there is more convincing reason for me to do.