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Measuring the size distribution of small (kilometre-scale) Kuiper belt objects (KBOs) can help constrain models of Solar system formation and planetary migration. Such small, distant bodies are hard to detect with current or planned telescopes, but can be identified as sub-second occultations of background stars. We present the analysis of data from the Weizmann Fast Astronomical Survey Telescope, consisting of fast photometry of ∼106 star-hours at a frame rate of 10–25 Hz. Our pipeline utilizes a matched-filter approach with a large template bank, including red-noise treatment, and injection of simulated events for estimating the detection efficiency. The KBO radius at which our survey is 10 per cent (50 per cent) efficient is 1.1 (2.0) km. The data from 2020–2021 observing seasons were analysed and no occultations were identified. We discuss a sample of sub-second false-positive events, both occultation-like and flare-like, which are still not fully understood but could be instructive for future surveys looking for short-duration events. We use our null-detection result to set limits on the kilometre-scale KBO number density. Our individual radius bin limits are consistent with most previous works, with N(r > 1 km) ⪅ 106 deg−2 (95 per cent confidence limit). Our integrated (all size) limits, assuming a power law normalized to large (≈45 km) KBOs give a power-law index q < 3.93 (95 per cent confidence limit). Finally, our results are in tension with a recently reported KBO detection from the ground, at the p = 4 × 10−4 level.