Weyrwoman -- Prima
Weyrleader -- Primus

Prima ? & Primus Reikaee

Weyrwoman's 2nd -- Optima
Weyrleader's 2nd -- Optimus

Optima ? & Optimus ?

Wingleader -- Dux
Wingsecond -- Optio
Wingrider -- Alaris
Wing -- Ala

Dux Sol, Ala DragonHeart
Optio Jorik, Thirteenth Ala (not the usual way of using ala, but the Thirteenth Ala used to be the Thirteenth Division, so they just traded 'Ala' for 'Division')
Alaris Aeran

Candidate -- Novo
Hatchling Level -- Tiro
Weyrling Level -- Paro
Rider (Adult Level) -- Draconar

Novo Rekkar
Tiro Winter or Winter, Draconar Tiro
Paro Shy'aroin or Shy'aroin, Draconar Paro
Draconar Fyre

Weyrlingmaster -- Decurio
Assistant Weyrlingmaster -- Legatus
Searchrider -- Capio

Decurio Fyre
Legatus ?
Capio Deira, Capios Deira and Dorian

Watchrider -- Custos

Custos R'hiin

Lord -- Dominus
Lady -- Domina

None defined, as of yet

Weyr -- Nidus
weyr (individual quarters) -- Nidulus (singular) / Niduli (plural)
('apartments' 'chambers' 'quarters' 'rooms' are all acceptable)

Nidus Otykaii
Joker's Nidulus or "I'll show you to your Niduli"

Fortress (Dark Weyr) -- Arx
DarkWeyr wing - Vis (meaning: violence, force)