The Spanish Milled Dollar or eight reales are called “pieces of eight.” Sometimes they really were made into to pieces of eight, which was a way to make change. The trouble, how you know if the “pie piece” was made one or two centuries ago, or last week. This piece is an official piece of eight. It came from the island of Curacao which counterstamped these pieces to make them official. Still, this “pie piece” looks a little skimpy. Perhaps this was a “piece of nine” or ten, which was a problem in those days.
I won't swear to it but I think it means 3 stuiver. At the time, an 8 reales was worth 40 stuiver. So an eighth of an 8 reales would be 5 stuiver, and since as you said it's a bit small to be an eighth, I suspect it was countermarked with a 3 (stuiver) based on actual weight.
I could be way off base here, but I believe the word "piece" in "piece of eight" didn't originally mean a portion but a coin. For example, in French even today "une piece" means, among other definitions, a coin. A "fifty-cent piece" is a half dollar. Thus, a "piece of eight" would be a "coin of eight reales." That being true, what you have here is a piece of a piece of eight.
Nice coin! Here are my 2 pieces, both of mine are a cut 1/5th. I've bid on a few of some of the other islands but have so far been outbid, especially since I've not focused on these coins. I'd like to have a St. Lucia one next. This is the note from an old dealer tag of the Curacao coin.
It would be more commonly known as a bit. 8 reales coins were frequently cut into 8 bits. That is why quarters are still sometimes called two bits.
It does not show in the photo, but with this piece, they could have gotten 9 or 10 bits out of that dollar.
The (3) is a counterstamp signifying 3 reales. A shortage of local coinage prompted a division of the Spanish 8 reales into triangular sections often far smaller than would be their Spanish equivalent fractions. These chopped counterstamps began around 1799 and when the Curaçao coin regulations were implemented in 1827, the pieces counterstamped with (3) were one of the few old forms of currency legally allowed to still circulate. They circulated as half-guilder pieces for several years thereafter. This equates to 1/5 of the rijksdaalder (5 guilders = 1 rijksdaalder).