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Wiktionary
double bridle

n. A common term for a Weymouth bridle, that uses both a bradoon, held by a sliphead, and a curb bit, and is used with two reins.

Wikipedia
Double bridle

A double bridle, also called a full bridle or Weymouth bridle, is a bridle that has two bits and four reins (sometimes called "double reins"). One bit is the bradoon (or bridoon), is a modified snaffle bit that is smaller in diameter and has smaller bit rings than a traditional snaffle, and it is adjusted so that it sits above and behind the other bit, a curb bit. Another term for this combination of curb and snaffle bit is a "bit and bradoon," where the word "bit" in this particular context refers to the curb.