  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 $\ell_{\rm max}=4500$,
corresponding to significantly smaller scales ($\delta\theta\sim2.4'$) 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 $S_8\equiv\sigma_8\sqrt{\Omega_{\rm
m}/0.3}=0.795^{+0.015}_{-0.017}$, in relatively good agreement with CMB
constraints from Planck (less than $\sim1.8\sigma$ tension), although we obtain
a low value of $\Omega_{\rm m}=0.212^{+0.017}_{-0.032}$, in tension with Planck
at the $\sim3\sigma$ level. We show that this 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 $H_0$. 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
$\ell\lesssim2000$ 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
