Bideford are still looking for their first win, with two defeats in three days leaving them pointless after their first four games since stepping up into Southern league Premier Division football.
Despite some good displays, the higher class has seen the Robins struggle to match the scoring of their opponents.
At home to Bedworth Town on Saturday they gave as good as they got, and dominated for long periods.
But chances went just wide, just over the bar or were thwarted by the visiting keeper and they were unable to get the ball into the net.
In contrast, Bedworth opened their account after 10 minutes when Bessant forced the ball through a throng of players in a goalmouth scramble.
Skipper Matt Hockley and Sean Downing were unable to turn chances into an equaliser and Steve Orchard came close with a header, too.
Unlucky Orchard was then penalised when a ball blasted towards him hit an arm and he was adjudged to have handled. Keeper Paul Hider got a hand to Bessant’s spotkick, but could not prevent him from grabbing a second goal.
Bideford pressed hard in their efforts to get back into the game, but only for Fuller to put it beyond their reach with a third goal 15 minutes from the end.
There was a brighter start on Monday night as the Robins took the lead after 17 minutes away to Weymouth.
A through ball from ian Sampson spli the home defence and Ellis Laight - giving Kevin Squire a rest from the front-running role - slotted it home.
Weymouth drew level on 26 minutes through former Torquay youth player Scott Joyce, but Bideford were still holding their own at the interval.
Former Bideford player Craig Duff blasted Weymouth in front from the edge of the area six minuted into the second half.
Matt Andrew tried to reply, but his shot went just over, and the game was then sealed when Joyce completed his hat-trick with two more edge-of-the-box shots in a 10 minute spell to put the hosts 4-1 ahead.
Bideford kept trying. A goalbound Steve Orchard header was well savedbefore he sent over a cross for Matt Hockley to head home for a final 4-2 scoreline.
With Aaron harper-Penman and Jack Furzer both out with injury, the Robins have problems at the back, which forced skipper Hockley to drop back for Monday’s game.
Manager Sean Joyce is now understood to be looking at two possible centre halves from South Devon to help plug the gaps and also the possiblility of another young Plymouth Argyle first year professional - a striker - to follow the path of Jed Harper-Penman to Bideford.