"Tri-State Weather" was a segment that only New York City area cable subscribers and all satellite viewers would have seen, except for erroneous situations.
It aired at 4:57, 5:27, 5:57, and 6:27 pm every evening.
Viewers that didn't see "Tri-State Weather" (ie. is most of you) saw a three minute local forecast, which played over the national feed.
"Tri-State Weather" debuted in October 1987.
Coincidentally, this was also the time the three minute local forecast was introduced.
I guess you could say the three minute local forecast was a trade off.
Both groups got a more in depth look at their local conditions and forecast.
So far I haven't come across a promo announcing the debut of the segment, but I do have one announcing the debut of the 3:00 local forecast.
I also have an example of the segment, in case you've never seen it.
Here are the video clips I mentioned above.