Perhaps I shouldn't have used the word weakness. But if they're driving style is similar, something which adversely affects one is likely to adversely affect the other. Perez was very consistent first half of the season...not so second half. And I think Button does make mistakes, no loads, but he makes them.
And remember who it was that took the team in the wrong direction on set up last year, there won't be a Hamilton in the other car whose settings they can default to and who will be bringing the points home while it all gets sorted out. Button is leading this, he's said so frequently, so if he gets it wrong this year , Perez will also be affected. He might not of course, and then Perez will indeed be in with a good chance of the championship.
Without getting too into semantics i think weakness is an apt term, i just think they have different weaknesses. And when i say mistakes i mean on track errors, in this instance. I think you are being a bit harsh on Button saying "And remember who it was that took the team in the wrong direction on set up last year" considering a race like Spa where his side nailed it and Hamilton's side went completely in the wrong direction, for an example. That's not to say i think he's some genius or whatever though before anyone goes off at me, cause the problems at Canada and Monaco, etc, were obvious.
Regardless of that, i don't think Perez will just use Button's setups all the time next season if that is what you are implying, the teams don't work like that (ie automatically just using one baseline setup), the drivers will always devlop their own setup tweaks at the track, and only default to the other drivers' setup when there is some crisis at the last minute. I believe Perez might turn out to be very capable of managing by himself without just doing what Button does anyway

While i'm here one thing i don't get, this constant thing that seems to appear round here about how Button can only go quick when the car is
perfect, cause that is completely at odds with his long proven skill in wet and changing conditions, where the car handles at its worst.