In a game played in driving rain and a swirling wind both sides found it difficult to gather any momentum as the conditions dominated.
As the ball swung from end to end after a series of mis-placed, over-hit passes chances were at a premium in the opening stages.
Michael Twiss tried his luck in the first minute with a volley from the edge of the box that was easily gathered by keeper Aaron Lee-Barrett and, after a neat move involving Wayne Curtis and David Perkins, striker Danny Carlton looked set to run free on goal but was pulled back by a marginal offside.
Weymouth then began to get a foothold in the game in midfield and Morecambe keeper Ryan Robinson did well to race from his line and save at the feet of Raphael Nade who looked to run on to a dangerous throughball.
As Weymouth pressed they thought they had taken the lead when Nade headed an excellent Abdou Elkholti cross past Robinson only to see the effort ruled out for a push.
A minute later the Terras again went close to taking the lead when a Simon Weatherstone shot from the edge of the area grazed the right-hand post with Robinson beaten.
Alerted by the scare Morecambe came back and forced a series of corners. From the first Danny Carlton saw a header deflected inches wide by Simon Downer but from the second the Shrimps took the lead.
Twiss' inswinger was flicked on by Chris Blackburn and Danny Meadowcroft was on hand six yards out to slot home the loose ball for his first goal for the Shrimps.
Downer almost replied for the visitors with a vicious dipping shot that just evaded the crossbar before half-time.
There was no let-up for the players in the second half as the rain continued to pour, making life even more difficult. Despite that there was no lack of effort from both sides with Morecambe starting the period brightly.
Carlton was close to heading home a dangerous Gary Thompson cross and Elkholti produced a vital defensive clearance to deny Thompson a free run on goal.
At the other end there was a sniff of a chance for Downer as the ball just failed to sit up for him on the edge of the box before the turning point of the game. Nade broke free of the Morecambe defence and created a great opening only to be denied by an excellent save from Robinson.
It was a save that proved vital as Morecambe added a second on the hour. After being gifted a corner by Lee-Barrett, who let a long-range shot squirm from his grasp, the Shrimps extended their lead.
Twiss was the provider again with a ball to the near post and Curtis stole a march on his marker to deflect the ball into the top right-hand corner of the Weymouth goal.
The excellent Twiss had a chance to add to his impressive goal tally for the season but drove an effort wide after wrestling free of Ashley Vickers and Garry Hunter let fly from distance with a shot that crept wide of the left-hand post. The Terras piled bodies forward towards the end but the Morecambe defence held firm.
Weatherstone gave them a brief scare with a 25-yard effort and Dean Howell struck a free-kick in a dangerous position into the wall before the final whistle went to give Morecambe a welcome three points.