The Weinstein claims, like the claims here, were basically he-said/she-said claims. There wasn't supporting physical evidence, etc. Republicans were eager to believe, even when just the first few came out, because Weinstein was a well-known liberal. Now they'd like to impose a totally different standard, because it's one of their boys.
In what sense do you think Dems have abused this? Three women have each come forward, of their own accord, and accused Kavanaugh of serious sexual misconduct against them. One has agreed to testify about it under oath. Another has signed a sworn affidavit. What are the Democrats supposed to do, in your mind? Should they say "sorry -- unless you've got hard evidence, we have no interest in hearing your story"?