Hazards in AFT with Weibull distribution

As this source notes:

the Weibull is the only distribution that is closed under both the accelerated life and proportional hazards families.

So if you are working with a distribution in the Weibull family (that includes simple exponential models), then you can model with either a proportional hazard (PH) or an accelerated failure time (AFT) model, and you will still end up with a Weibull distribution. In that sense, whenever you use an AFT model with an underlying Weibull distribution, the PH assumption will hold--and vice versa. For distributions outside the Weibull family, at most of one of AFT or PH can hold.