We present a cosmological analysis of the combination of the DES-Y3, KiDS-1000 and HSC-DR1 weak lensing samples under a joint harmonic-space pipeline, using angular scales down to ℓ_max = 4500, corresponding to significantly smaller scales (δθ ∼ 2.4'). We accurately model non-linearities and baryonic effects using Baccoemu. We find S_8 ≡ σ_8√(Ω_m/0.3) = 0.795_{-0.017}^{+0.015}, in relatively good agreement with CMB constraints from Planck (less than ∼1.8σ tension), although we obtain a low value of Ω_m = 0.212_{-0.032}^{+0.017}, in tension with Planck at the ∼3σ level. This tension can be recast as an H_0 tension if one parametrises the amplitude of fluctuations and matter abundance in terms of variables without hidden dependence on H_0. Including a prior on the distance-redshift relationship from BAO data reduces this tension significantly without worsening the fit. Baryonic effects have a mild impact on HSC-DR1 but not on DES-Y3 and KiDS-1000. We show that our ability to mildly constrain the parameters of the Baryon Correction Model with these data is in agreement with this finding. We compare our results with official analyses of DES-Y3 and KiDS-1000, finding good agreement with the official results, despite differences in analysis choices. We find that using the non-linear matter power spectrum from Baccoemu leads to a higher S_8 than HALOFIT. We also compare our results with the official analysis of DES-Y3 + KiDS-1000, finding good agreement with the official results, albeit with a mild shift on S_8 of about 0.6σ. Differences are expected due to different analysis choices, including different summary statistics and modelling of the matter power spectrum and baryon effects. We find that the parameter shifts we observe are in agreement with known discrepancies between real and harmonic-space analyses.We present a cosmological analysis of the combination of the DES-Y3, KiDS-1000 and HSC-DR1 weak lensing samples under a joint harmonic-space pipeline, using angular scales down to ℓ_max = 4500, corresponding to significantly smaller scales (δθ ∼ 2.4'). We accurately model non-linearities and baryonic effects using Baccoemu. We find S_8 ≡ σ_8√(Ω_m/0.3) = 0.795_{-0.017}^{+0.015}, in relatively good agreement with CMB constraints from Planck (less than ∼1.8σ tension), although we obtain a low value of Ω_m = 0.212_{-0.032}^{+0.017}, in tension with Planck at the ∼3σ level. This tension can be recast as an H_0 tension if one parametrises the amplitude of fluctuations and matter abundance in terms of variables without hidden dependence on H_0. Including a prior on the distance-redshift relationship from BAO data reduces this tension significantly without worsening the fit. Baryonic effects have a mild impact on HSC-DR1 but not on DES-Y3 and KiDS-1000. We show that our ability to mildly constrain the parameters of the Baryon Correction Model with these data is in agreement with this finding. We compare our results with official analyses of DES-Y3 and KiDS-1000, finding good agreement with the official results, despite differences in analysis choices. We find that using the non-linear matter power spectrum from Baccoemu leads to a higher S_8 than HALOFIT. We also compare our results with the official analysis of DES-Y3 + KiDS-1000, finding good agreement with the official results, albeit with a mild shift on S_8 of about 0.6σ. Differences are expected due to different analysis choices, including different summary statistics and modelling of the matter power spectrum and baryon effects. We find that the parameter shifts we observe are in agreement with known discrepancies between real and harmonic-space analyses.