I have found that correct stretching in between sets for weight training has been very beneficial.
Either stretching the muscle you are training or corrective stretching.
By corrective I mean that if you are doing bridges working someones glutes then if you stretch their hip flexors in between sets then they will be able to get a fuller range of movement while doing the bridge if their hip flexors are tight. You have to flex the hip to do bridges and if someone has tight hip flexors, psoas major, minor and illiacus then they will have limited range of movement while doing a bridge. Meaning they won’t be able to push their butt up as high as possible.
Or stretching calves before squats if the calves are tight. Or stretching the chest in between sets of rear delt raises. Think of the antagonist (opposite) muscle and if it is tight then stretch it before doing the agonist (If the goal is fuller range of movement).
I have found that lighter the tension on the stretch the better than the so called deep stretch. Just my opinion.
Oh by the way, remember that the opposite muscle will not really be warmed up so it won’t stretch as well as the muscle you are working on.
Also, as a general rule some muscles that are long and weak will not need as much stretching as muscle that are short, strong and tight. Which the short tight ones may need foam rolling as well.