We present a 1.3mm continuum survey of the young (2-3Myr) stellar cluster IC 348 that lies at a distance of 310pc and is dominated by low-mass stars (M*~0.1-0.6M_{sun}_). We observed 136 Class II sources (discs that are optically thick in the infrared) at 0.8arcsec (200au) resolution with a 3{sigma} sensitivity of ~0.45mJy (M_dust_~1.3M_{Earth}_). We detect 40 of the targets and construct a mm-continuum luminosity function. We compare the disc mass distribution in IC 348 to those of younger and older regions, taking into account the dependence on stellar mass. We find a clear evolution in disc masses from 1 to 5-10Myr. The disc masses in IC 348 are significantly lower than those in Taurus (1-3Myr) and Lupus (1-3Myr), similar to those of Chamaleon I, (2-3Myr) and {sigma} Ori (3-5Myr) and significantly higher than in Upper Scorpiusrpius (5-10Myr). About 20 discs in our sample (~5 percent of the cluster members) have estimated masses (dust+gas)>1M_Jup_ and hence might be the precursors of giant planets in the cluster. Some of the most massive discs include transition objects with inner opacity holes based on their infrared Spectral Energy Distribution (SEDs). From a stacking analysis of the 96 non-detections, we find that these discs have a typical dust mass of just <=0.4M_{Earth}_, even though the vast majority of their infrared SEDs remain optically thick and show little signs of evolution. Such low-mass discs may be the precursors of the small rocky planets found by Kepler around M-type stars.