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 making use of angular scales down to ℓmax=4500, corresponding to significantly smaller scales (δθ ~ 2.4') than those commonly used in cosmological weak lensing studies. We are able to do so by accurately modelling non-linearities and the impact of baryonic effects using Baccoemu. We find S 8 ≡ σ 8√(Ωm/0.3) = 0.795+0.015 -0.017, in relatively good agreement with CMB constraints from Planck (less than ~1.8σ tension), although we obtain a low value of Ωm =0.212+0.017 -0.032, in tension with Planck at the ~3σ level. We show that this can be recast as an H0 tension if one parametrises the amplitude of fluctuations and matter abundance in terms of variables without hidden dependence on H0. Furthermore, we find that this tension reduces significantly after including a prior on the distance-redshift relationship from BAO data, without worsening the fit. In terms of baryonic effects, we show that failing to model and marginalise over them on scales ℓ ≲ 2000 does not significantly affect the posterior constraints for DES-Y3 and KiDS-1000, but has a mild effect on deeper samples, such as HSC-DR1. This is in agreement with our ability to only mildly constrain the parameters of the Baryon Correction Model with these data.