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The main armament of the Heavy Raider seems to consist of a barbette of six cannons mounted under the cockpit area of the vehicle (as seen here). These cannons are capable of an extremely high rate of fire (Scattered). The Heavy Raiders are also capable of launching missiles.
The first Heavy Raider is seen as part of a Cylon search party looking for Karl "Helo" Agathon and Sharon Agathon née Valerii on Cylon-occupied Caprica (Tigh Me Up, Tigh Me Down). Further sightings in Season 1 are in "Colonial Day" with one craft landing near Agathon and Valerii, and in space over Caprica in "Kobol's Last Gleaming, Part II".
After shooting down a Colonial scouting party over Kobol, a force of five Centurions lands near the crash site of Raptor 1 in a Heavy Raider. They proceed to dismantle its missile launcher and DRADIS assembly in an attempt to build a surface-to-air missile battery, intending to shoot down any search and rescue parties that Galactica sends to find the survivors (Fragged).
The Heavy Raider is conclusively proven to be a troop transport in "The Farm" when Sharon Agathon née Valerii commandeers one and uses it to evacuate the Caprica Resistance after they rescue Kara Thrace from a Cylon hybrid "farm." That captured Heavy Raider is eventually used to jump to Kobol where Thrace, Agathon and Valerii finally hook up with Laura Roslin's fleet.
The Cylon attack fleet in "Flight of the Phoenix" includes a large amount of Heavy Raiders, which could indicate a planned boarding operation or merely the need for additional heavy firepower.
Months later, Felix Gaeta reveals that with Valerii's cooperation they are able to interface the navigational system of a captured Heavy Raider with a Raptor's FTL drive, making it capable of farther and more accurate jumps than before (beyond Colonial FTL's Red Line limit) with significantly faster calculations (as previously determined from a captured Cylon Raider). A strike team is able to return to Caprica in less than ten jumps and successfully rescues the Caprica Resistance (Lay Down Your Burdens, Part I).
After New Caprica, Thrace believes she sees a Heavy Raider in the atmosphere of a nearby gas giant, although no one else can see it. Its appearance may somehow relate to her alleged destiny (Maelstrom).
Heavy Raiders play a significant part in the battle to destroy the Cylon Resurrection Hub. Piloted by rebel Cylons, they tow powered-down Colonial Vipers to get them close without their engines and electronics being detected. After the cables are cut and the Vipers' systems activated, they engage the Cavil-faction baseships and Raiders until the resurrected D'Anna Biers is retrieved and the Vipers destroy the Hub in a nuclear missile strike (The Hub).
A Heavy Raider is seen running a joint CAP with Colonial Vipers in Deadlock.