This is law in many states. I set up an LLC in Maricopa county in AZ and it was required to publish an ad in at least two local newspapers. I asked repeatedly about doing an online ad, but they said it was a law so too bad.
The 6 weeks requirement is arbitrary and onerous - if the public was not sufficiently informed after 2 weeks or 4 weeks, is it going to be informed after 6 weeks? Likewise, the law journal requirement is arbitrary and onerous - the journal has no public readership whatsoever so it cannot claim to achieve the purpose of informing the public about your new LLC, nor can it justify the exorbitant advertising fee.
Over the years, there have been multiple lawsuits to repeal the requirement but nothing has changed. It's a money issue, as usual - the media lobby is strong and wants to hang on to these bogus fees. By the way, it takes exactly two minutes to find any LLC on the official NYS website, and it's free.