On Earth, the velocity at which subducting plates are consumed at their trenches (termed “subduction rate” herein) is typically 3 times higher than trench migration velocities. The subduction rate is also 5 times higher than estimated lower mantle slab sinking rates. Using simple kinematic analyses, we show that if this present-day “kinematic state” operated into the past, the subducting lithosphere should have accumulated and folded beneath near-stationary trenches. These predictions are consistent with seismic tomography, which images localized and widened lower-mantle slab piles. They are, however, at odds with most dynamic-subduction models, which predict rapid trench retreat and inclined slabs in the mantle transition zone. We test the hypothesis that a weak asthenospheric layer (WAL), between the lithosphere-asthenosphere boundary and 220 km depth, compatible with geophysical constraints, can remedy the discrepancies between numerical models and observations. The WAL lubricates the base of the lithosphere, increases the subduction rate while reducing trench retreat. As a consequence, simulations featuring a WAL predict slab accumulation at the mantle transition zone, and thicker, folded slabs in the lower mantle. A WAL viscosity only 2–5 times lower than that of the adjacent mantle is sufficient to shift subduction regimes toward a mode of vertical slab sinking and folding beneath near-stationary trenches, across a wide range of model parameters, producing surface and slab velocities close to those observed at the present-day. These findings provide support for the existence of a weak asthenosphere beneath Earth's lithosphere, complementing independent evidence from various geophysical data.