Doubled - To give it stability, or to form what was used as a bag for the Urim and Thummim: the latter appears to be the more likely.

Four-square it shall be - Here we have the exact dimensions of this breastplate, or more properly breast-piece or stomacher. It was a span in length and breadth when doubled, and consequently two spans long one way before it was doubled. Between these doublings, it is supposed, the Urim and Thummim were placed. See Clarke on Exodus 28:30 (note).

(i) Foursquare it shall be [being] doubled; a span [shall be] the length thereof, and a span [shall be] the breadth thereof.
(i) The description of the breastplate.

Four square it shall be, being doubled,.... That is, when it was doubled; for the length of it, according to Maimonides (c), was a cubit, which is two spans, and so, when it was doubled, was but one, and its length and breadth being alike, as follows:
a span shall be the length thereof, and a span shall be the breadth thereof; a square, which is the measure, the form of the new Jerusalem, the church of Christ, Revelation 21:16 and may denote the perfection, firmness, and immovableness of it, Psalm 125:1. Some have thought that this breastplate was doubled, in order to have something enclosed in it: some imagine, that within this fold were put the Urim and Thummim, which they suppose to be two words engraved on a stone, and different from the twelve stones in it; others, that the name of Jehovah was written and put there, as the Targum of Jonathan and Jarchi on Exodus 28:30 and other Jewish writers, and others, fancy some little images were put within these folds, the name with the teraphim, and supposed to be the Urim and Thummim; but if these were hid in the folds, they could not be seen when consulted; it is most probable there is nothing put within the double, which was not done for any such use; but most likely that it might be strong to bear the weight of the precious stones, put in ouches of gold upon it.
(c) Cele Hamikdash, c. 9. sect. 6.