After Harris was caught off his bowling, Caleb O'Connell tore through the lower order to finish with 4-24 in a six over spell, after Paora O'Donnell (2-17) did the early damage and Adam Simonsen (3-32) got the key scalps of Ford and both Rayners.
In reply, Weraroa were under pressure at 13-3, with Dominic Rayner (3-32) getting back-to-back wickets in the third over.
But Simonsen (33) steadied the ship, and Josh Shaw (56 not out) hit eight boundaries to have victory in sight when the weather packed in.
The loss leaves Marton at long odds to reach the semifinals with two games remaining, although they will approach playing winless Marist with some confidence next weekend at Centennial Park.
St Johns Tech and Property Brokers United will face each other at Victoria Park.
Scoreboard
Marton 162 (J Harris 85, C Rayner 23, C O'Connell 4-24, A Simonsen 3-32) lost to Weraroa 144-5 (J Shaw 56no, A Simonsen 33, D Rayner 3-32) via Duckworth-Lewis method.