An observationally-constrained time series of historical aerosol effective radiative forcing (ERF) from 1750 to 2019 is developed in this paper. We find that the time history of aerosol ERFs diagnosed in CMIP6 models exhibits considerable variation and explore how the time history of aerosol forcing influences the probability distributions of present-day aerosol forcing and emergent metrics such as climate sensitivity. Using a simple energy balance model, trained on CMIP6 climate models and constrained by observed near-surface warming and ocean heat uptake, we derive estimates for the historical aerosol forcing. We find 2005-2014 mean aerosol ERF to be -1.1 (-1.7 to -0.5) W m-2 relative to 1750. Assuming an SSP2-4.5 forcing pathway, aerosol ERF in 2019 is -0.9 (-1.5 to -0.4) W m-2. There is no strong trend in aerosol forcing between 1972 and 2014. This analysis also gives a 5-95% range of equilibrium climate sensitivity (ECS) of 1.9-6.0C (best estimate 3.1C) with a transient climate response (TCR) of 1.3-2.7C (best estimate 1.8C). We find TCR is not sensitive to the historical aerosol forcing time series used for constraint, although the upper bound of ECS is difficult to constrain this way.