The Terras put up a brave fight at the Wessex Stadium and created several fine openings but the impressive Shots were more clinical in the final third and thanks to strikes by Rob Elvins and Jonny Dixon are now one point clear of second-placed Torquay United who play this afternoon.
Weymouth boss Jason Tindall fielded two new signings in his starting XI.
AFC Bournemouth defender Neil Young, who has joined on a month's loan, began in the centre of defence while Callum Hart started at left back in place of Narada Bernard.
The youngster, who was with the Cherries last season, has signed non-contract terms.
With Justin Roberts ruled out through suspension, Joel Kita-mirike retained his place and partnered Young at the heart of the back four while Conal Platt again kept out leading scorer Jefferson Louis, who began on the bench.
It was the Shots that looked the better team in the opening exchanges. Joel Grant made a fine break down the left and nearly found Elvins unmarked in the box before visiting skipper Rhys Day headed wide from a corner.
Platt was occupying a position just behind Gavin McCallum in a 4-4-1-1 formation for the Terras and Town were certainly struggling to pick him up.
James Coutts put McCallum down the left on seven minutes and his driven cross just missed out Platt and Nick Crittenden who had both made fine late runs into the box.
Two minutes later Aldershot threatened again through winger Grant. His incisive pass found Dixon but home keeper Jon Stewart was out quickly to block the ball to safety.
Suddenly Weymouth were looking under pressure and Stewart soon had to come to the rescue again, pushing wide a fine strike by Ben Harding.
Louie Soares was the next to threaten for the visitors when he sliced wide from inside the box but the hosts continued to weather the storm and soon began to look a little more composed.
But it was the still the visitors who were enjoying the majority of the possession and on 24 minutes only a timely interception by Young stopped Grant's low cross from reaching the unmarked Elvins.
The Terras were looking like the away team, soaking up pressure and trying to hit their opponents on the break, and on a couple of occasions they had the Shots stretched but their final ball often let them down.
Weymouth began to enjoy their first good spell but it was brought to a premature end on 33 minutes after Scott Doe made a petulant challenge on the lively Grant near the left corner flag.
Scott Davies knocked in the resulting free-kick to the far post and when Hart was forced to clear the ball off the line after it was bundled towards the target, it fell to Elvins who drove home from 10 yards.
The hosts responded with Coutts driving a shot at Town keeper Nikki Bull but there was no doubt that Weymouth were going to have to be more adventurous in the second half if they were going to gain anything from the game.
With that in mind, Tindall brought on Stuart Beavon for McCallum but on 50 minutes Davies played in Soares who should have made it 2-0 but his shot went across the face of goal and wide of the far post.
Weymouth then made their best chance of the game when Anton Robinson broke down the left and put Coutts away. He squared the ball across to Platt who shot wide from close range under pressure from Bull.
It was a big chance missed for the Terras but they continued to come forward.
Beavon and Crittenden both had shots saved and Coutts was looking dangerous down the left but moments later Town grabbed their second to kill off the game.
The goal came just three minutes after Tindall took off Hart and replaced him with striker Jefferson Louis.
The switch saw Crittenden move from right wing to left back which perplexed many fans as the ex-Chelsea man was looking one of the Terras' biggest threats.
But Hart had received a knock and could not continue and with substitute Bernard not fully fit the hosts opted to try and go more offensive in search of a leveller.
Unfortunately for Tindall that decision backfired when on 70 minutes the Shots broke away after clearing a Weymouth corner.
There seemed no immediate danger when Dixon first received the ball on halfway but somehow he powered his way past Critten-den and Kitamirike before sliding the ball past the onrushing Stewart.
Weymouth just huffed and puffed after that and on the balance of play it was the visitors who fully deserved their three points.
Reporter: Adam Summers