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The capacity of surveys like Euclid to provide meaningful dark energy constraints is restricted by a limited theoretical understanding of the role of baryonic physics in large scale structure, namely the effects of adiabatic contraction, and supernova and AGN feedback in dark matter haloes. This work adopts a halo model that broadly parameterises the baryon impact through three characteristic features of the NFW profile: the concentration amplitude; the dependence of the profile on halo mass; and small-scale behaviour via flat, baryon-induced cores (instead of cusps). An in-depth Fisher analysis for the weak lensing power spectrum implies that significant degeneracies between this latter effect and cosmological parameters are largely limited to the spectral index. Conversely, forecasts for the dark energy parameters themselves are minimally compromised, supporting a case for optimism. The analysis also allows one to answer the inverse question and forecast constraints on baryon effects themselves as the era of precision cosmology advances. Ultimately these sets of results are subject to more profound questions of model bias, though calibrating expansions of baryon parameters in terms of halo mass is shown to be one of the most promising routes towards mitigating this concern. Nevertheless, the issue becomes increasingly sensitive when extending the analysis to include the additional impact of neutrinos and the wider scope of modified gravity cosmologies.