I believe that Littlefinger is his real father, not Jon Arryn. Evidence for this:

* Jon Arryn when young was a strong man with blond hair. He looks weedy and has black hair like Petyr

* It's implicit Petyr and Lysa were having an affair. He claims to have taken both Tully sister's maidenhead. One of those times was Lysa tricking him, so he must have willingly slept with Lysa

* Of his other marriages and long life Jon never had children. The most was one stillbirth, suggesting he's mostly infertile