A Feeble or Weakest version of the Berolina Pawn would have to start the
game aimed to move diagonally towards or across the center line.
The thing about Berolina Pawns is that they attack fewer squares but have
more mobility, and therefore are very difficult to block from promotion in
many endgames.
K+Berolina versus K is always a win except in the degenerate case of K
takes P, and except in the case Ka6 Pa7 K(b8 or c8).
Reasoning from this, I'd expect that the Feeble/Weakest Berolina Pawn
would be quite strong. The weakness of the enemy pieces would often allow
it to make a run for the goal line.