http://imgur.com/0UZ0TY0,gDuPrMK,UjIehew
I found this gravestone in Worcester MA, and can't identify the symbol on it. Is it advocated with freemasonry somehow? (I see the Freemason symbol in the other corner of the grave)
Imgur is being screwy, I can see 3 pictures in the album. Here's a photo of the specific stone
This appears to be variant of the symbol for the Order of the Eastern Star (OES). OES is a woman's auxiliary of the Freemasons. The inverted star with the altar in the center is their primary symbol. The different points represent different virtues, usually represented by emblems which would be too small to carve recognizably in their space on the stone. Here they are represented by letters, though I'm not sure what the mapping is of those particular letters to their symbols.
See http://www.ohiooes.org/the-star
Source: I'm a Mason, but not involved in OES.
In order to save us having to remove dozens of comments in the near future, I'm just going to mention here that those letters seem to spell "fatal".
With that out of the way, we can all now wait for someone to provide an in-depth and comprehensive answer to your question.
You seem to have uploaded the incorrect picture, the one you linked is a modern stone.