Operational stability of perovskite solar cells (PSCs) is rapidly becoming one of the pressing bottlenecks for their upscaling and integration of such promising photovoltaic technology. Instability of the hole transport layer (HTL) has been considered as one of the potential origins of short life-time of the PSCs. In this work, by varying the molecular weight (MW) of doped poly(triarylamine) (PTAA) HTL, we improved by one order of magnitude the charge mobility inside the HTL and the charge transfer at the perovskite/HTL interface. We demonstrate that this occurs via the enhancement of polaron delocalization on the polymeric chains through the combined effect of doping strategy and MW tuning. By using high MW PTAA doped combining three different dopant, we demonstrate stable PSCs with typical power conversion efficiencies above 20%, retain more than 90% of the initial efficiency after 1080 hours thermal stress at 85 ⁰C and 87% of initial efficiency after 160 hours exposure against 1 sun light soaking. By using this doping-MW strategy, we realized perovskite solar modules with an efficiency of 17% on an active area of 43 cm2, keeping above 90% of the initial efficiency after 800 hours thermal stress at 85 ⁰C. These results, obtained in ambient conditions, pave the way toward the industrialization of PSC-based photovoltaic technology.