Moore makes you feel for him and, at the same time, she makes you want to push off the weight of Ira — all his exposed, sappy neediness — far away.
Source (emphasis mine)
I think this way.
It can be rewritten thus: "push the weight off of Ira" meaning "get rid of the weight from Ira."
To say "the weight of Ira" is "Ira's weight" is ungrammatical in my opinion. When "the" is involved, like this, it's normal to say "A's B"
So from this perspective, to interpret this "of" as possessive is wrong.
Am I right?