I don't think it makes them weak at all. If anything, it is a strength. Predators have trained their whole lives for combat & for the hunt, their pride & honour reflects that. It makes them a much more worthy opponent because they will not use underhanded tactics to win a fight, & they will use all measures to make that fight as fair as it possibly can be.
On occasion though they will give their opponent time to recouperate themselves during a fight, while they see this as fair play, it is, in my opinion, a tactical disadvantage. In the original predator, he had Durch beat, he was crawling on his stomach, at the creature's mercy. But the predator let him live long enough to recoupererate himself, & fell into his trap.
The same in predator 2. Harrigan was wounded on the floor & could have been finished off in an instant. But the pred bided his time which allowed harrigan to deliver the blow to the stomach with the smart disc that killed him.
Probably the most talked about scene though is in AVP, where celtic had grid ensnared in the net & could have easily finished him off. But instead, he let him recouperate, he walked slowly up to him, taking his time. By the time he had even drawn his dagger, grid's blood had burned through the net & he was upon him.
This can be a major weakness in a 1 on 1 fight. Although preds don't always do this, it can be a fatal mistake if they do. Although this is a rare occurence, it is one downfall of the honour code, that they may be too leniant to their prey & all too eager to make themself vulnerable in order to even up the fight.