Preston strike Stuart Beavon pounced during the second-half of a match which leaves United still languishing in the relegation zone and Weir, who only took charge in June, battling to save his job.
Jose Baxter forced Declan Rudd to make a flying save at the near post after unleashing an angled drive while the Preston goalkeeper was called into action again soon when Tony McMahon went close from a set-piece.
Febian Brandy and Matt Hill both tried their luck from long-range as United continued to press but the latter was responsible for the slip which allowed Preston to take the lead against the run of play.
Kevin Davies, profiting from the defender's stumble, found Beavon lurking inside the area and he cut inside to beat George Long from close-range.
Weir said: "It's just so disappointing to watch that. We couldn't fault the lads for effort and I actually thought we were the better team. But that's the way it goes sometimes when you are down at the bottom.
"It's a test of character but, genuinely, I do not feel we are that far away. We just have to show the strength of character required to get out of this run and start winning games again.
"So much of what we are doing is right. But I appreciate, ultimately, it is all about results.
"You always question yourself and everything you do in situations like this.
"But, to be honest, it's difficult to pick apart what the lads do. We've just got to come back in on Monday morning and start working hard all over again.
"Because, if we do that, then I am sure it will start to happen for us."
- Sports & Recreation
- Marlon King
- Declan Rudd