Mr. Burleigh is one of the owners of the weapons manufacturing business Burleigh & Stronginthearm and President of the Armourers' Guild . He seems to be the sales and management half of the partnership. He sweated a lot when cross-examined by Vetinari concerning recent large sales of the firm's products to Klatch immediately prior to the outbreak of football, revealing that the weapons business was in fact a business and that unlike Ankh-Morpork, Klatch had a lot of both money and bandits/Morporkians to pacify.
In Jingo, the sales to Klatch listed by Vetinari include: The 'Great Leveler' Cart-Mounted Ten-Bank 500-pound Crossbow, the 'Meteor' Automated Throwing Star Hurler, (which can fully decapitate at twenty paces, money back if not fully decapitated) and the 'Dervish' Mk III Razor-Wire Bolas. In addition to this, Captain Carrot later found crates of 'Viper' Mk. 3 crossbows (which kill people but leave buildings standing) on a ship bound for Klatch.
A Lord Burleigh is referenced in Mrs Bradshaw's Handbook, as a man who in times past was responsible for breeding some lively and belligerent varieties of brassica.
Rincewind said in Sourcery to Coin, that his half-brick in a sock "kills people but leaves buildings standing." This phrase, in Roundworld, was commonly applied to the neutron bomb, which was designed to focus more on radiation effects than the blast and heat of a normal nuclear weapon.