A judge can't really say,"stop objecting"--due process of law and all that. However, I have seen judges say (while the jury is out), "Don't you see that the jury thinks you're hiding something? My advice is to keep the objections to a minimum," or, "Look, here's what hearsay means: [explains rule]. Please don't object again unless it fits within that definition."
Yes just logically speaking, if I was a juror and one side kept hopping up and objecting every time the other side brought something up, I would think the objecting side had something to hide or really didn't want something bad to come in, even if that wasn't the case.