Is the Parham inherently weak, or is it in ill-repute because mostly lower-rated players use it?
Yes.
I assume you meant that as a "yes" to both questions - I think, however, the folks are having fun debating it.
Well, not so much folks, as the one guy that make another account every so often and baselessly promotes it.
Of course I've seen this opening lots (ok, way too much), but never knew it was called the Parham. So who was Mr. Parham and does the poor guy's family tend to downplay his shining contribution to chess?
As for me, occasionally I enjoy watching a couple of real ~800 rated players play, as I stand there with clenched fists screaming at the monitor "HIS ROOOOOOK, IT'S RIGHT THERE, SNAP IT OFF!!! NOOOOOOOOO, NOT THE PAWN!!! AAYYIIIIIEEEEE!!