We present the results from a large 850um survey of the {sigma} Orionis cluster using the SCUBA-2 camera on the James Clerk Maxwell Telescope. The 0.5 diameter circular region we surveyed contains 297 young stellar objects with an age estimated at about 3Myr. We detect nine of these objects, eight of which have infrared excesses from an inner disc. We also serendipitously detect three non-stellar sources at >5{sigma} that are likely background submillimetre galaxies. The nine detected stars have inferred disc masses ranging from 5 to about 17M_Jup_, assuming similar dust properties as Taurus discs and an interstellar medium gas-to-dust ratio of 100. There is a net positive signal towards the positions of the individually undetected infrared excess sources indicating a mean disc mass of 0.5M_Jup_. Stacking the emission towards those stars without infrared excesses constrains their mean disc mass to less than 0.3M_Jup_, or an equivalent Earth mass in dust. The submillimetre luminosity distribution is significantly different from that in the younger Taurus region, indicating disc mass evolution as star-forming regions age and the infrared excess fraction decreases. Submillimetre Array observations reveal CO emission towards four sources demonstrating that some, but probably not much, molecular gas remains in these relatively evolved discs. These observations provide new constraints on the dust and gas mass of protoplanetary discs during the giant planet building phase and provide a reference level for future studies of disc evolution.