If there were villains in this story, Gloria's parents would be those villains. That is, they're the ones who get rid of Robbie. But, of course, they're not trying to be villainous—they just happen to choose the wrong option as parents. So they're the ones who put this story into motion by getting rid of Robbie; but they're not particularly original characters in any way.
That is, Grace Weston is a typical character: she's the housewife who cares what the neighbors think (75); she can't admit that she's wrong to her husband (122); and she kind of nags her husband. This is a stock character that you can probably find all over stories from this time period.
Likewise, George Weston is the typical husband character: he loves his wife and he likes taking things easy. And even though he wants to disagree with his wife in the case of Robbie, he knows that would interrupt his easy-going lifestyle. Honestly, if you flipped through any story from the 1940s, you'd find characters like this. (Or even from before: the whole nagging wife and easy-going husband characters can (sort of) be found in Jane Austen's Pride and Prejudice.)
In fact, it seems like Asimov uses really boring human characters here—kid Gloria, nagging wife Grace, too-easy-going husband George. Maybe he does use boring characters because then we're not focusing on them, but on the new, more interesting character of the robot.