The home side have reached the opening round for the first time in 15 years, while Wimbledon made the third round last season, before losing to Boreham Wood.
Match preview
Weymouth are experiencing a torrid campaign up until this point, as they currently sit rock bottom of the National League South.
They have only won one game this season - a 3-2 victory away at Slough Town - and Bobby Wilkinson's side are nine points adrift of safety in the league, so they will welcome the break from league affairs coming into this FA Cup clash.
Last time out, Weymouth were beaten comfortably by Dartford, courtesy of Alex Wall's brace and Joshua Johnson's strike in the opening quarter of an hour.
In fact, the success Weymouth have enjoyed this season has been in the FA Cup - they beat Winchester City in the second qualifying round, before beating Welling United and Havant & Waterlooville to set up Saturday's stunning home tie against the Dons.
Wilkinson will be hoping his side can put their league misfortunes to one side this weekend as they aim to cause an upset in front of their own fans.
Meanwhile, Wimbledon come into this clash unbeaten in their last three league clashes, sitting 15th in the League Two table.
However, they lost last time out on penalties against Portsmouth in the Football League Trophy. Pompey's 3-1 penalty shootout win earned them two points on the night - one more than the Dons - but both sides progressed to the last 32 of the competition with Wimbledon as group winners.
A brilliant individual goal from Ayoub Assal levelled matters on the night, after Ronan Curtis had given the hosts the lead.
Prior to that, late strikes from Courtney Senior and Josh Davison secured victory for the Dons against Harrogate Town to give them seven points from a possible 12 in their past four home games.
Johnnie Jackson's side made the third round of the FA Cup last year, so he will want to embark on a similar run this season, starting with a win on Saturday.
Weymouth FA Cup form:
Weymouth form (all competitions):
L
L
L
W
L
L
AFC Wimbledon form (all competitions):
L
L
W
D
W
L
Team News
Keelan O'Connell and Daniel Matsuzaka have been mainstays in Wilkinson's side this season, so it is expected that both players will feature on Saturday.
Nathan Carlyle was suspended against Dartford so he could return to proceedings here.
Tom Bearwish is the club's top scorer, finding the net on two occasions so far this season, but Wilkinson may opt for a different option up top for this game considering the Terras have only scored 10 goals in 14 games in the league.
As for the visitors, Johnnie Jackson made nine changes from the side that beat Harrogate in the Football League Trophy clash with Portsmouth on Tuesday, so it seems likely he will rotate his side once more for the FA Cup tie this weekend.
Luke Jenkins made a successful return from injury against Pompey so he could feature again here.
Josh Davison's late winner against Harrogate was his sixth goal of the season, so he will be keen to open his FA Cup account here.
Weymouth possible starting lineup:
Oualah; Howe, Carlyle, Matsuzaka, Kyprianou; O'Connell, McBurnie, Murray, Rose; Bearwish, Ash
AFC Wimbledon possible starting lineup:
Tzanev; Gunter, Kalambayi, Towler, Currie; Woodyard, Maghoma; Chislett, Pell, Assal; Davison
We say: Weymouth 0-3 AFC Wimbledon
It is hard to see anything other than AFC Wimbledon storming to victory here, considering Weymouth's form and the gap between the sides in the English football pyramid.