the basic argument being made is that even though I have considered Mr. Anonymous' arguments and decided they were without merit, I should still be significantly less certain of my position simply because a number of these anonymous people (making basically the same weak arguments) disagree with me. Did I misunderstand the argument being made?

Yes. The point is that in "deciding [the arguments] were without merit", you didn't take sufficient account of the quality (not merely the quantity, by the way) of the people making them.

If a high-quality person says "X is true", you might be able to dismiss it if you have sufficient knowledge. But if they say "X is true because of A,B, and C", you can't dismiss X without also dismissing A, B, and C. And here the problem is with your judgement about A, B, and C, not (just) your judgement about X.