The Seagulls took the lead after 12 minutes when former Bath player Shaquille Hunter fired past Luke Southwood.
The home side doubled their lead on the half-hour mark through Jake Lee at the second attempt after his initial effort had been blocked.
Two-nil at half-time can often be a dangerous lead, and Bath had their fans in the 591 crowd dreaming of a comeback when they reduced the deficit within 3 minutes of the restart when Ross Stearn’s free-kick struck the bar, only for Tom Smith to react quickest to the loose ball.
Bath did threaten an equaliser, but on 65 minutes the hosts were awarded a penalty which Gethyn Hill duly converted make it 3-1.
Weston made it 4-1 in the last minute of normal time when Jack Batten’s back pass beat his own keeper.
Ryan Case did manage to score a second for the visitors in the 4th minute of stoppage time, but by then most of their supporters had set off back up the M5.
Tuesday`s other game in the division saw Poole Town move out of the drop zone and to within a point of eighteenth-placed Chippenham Town at Tatnam.
The hosts were looking to follow up last Saturday`s fine 1-0 win at Hemel Hempstead Town, while the Bluebirds had drawn their previous two matches.
But it was the Dolphins who broke the deadlock 2 minutes before half-time with a goal from Mo Baghdadi.
Chippenham battled hard throughout but were unable to find a killer edge, and eventually saw Warren Bentley put the game beyond them when he netted Poole`s second from the penalty spot in the 71st minute.
(Photo:Simon Howe)