What are best practices for reviewing peer research lab colleagues' work for a supervisor? Since over a year, I've been involved in almost everything my supervisor does and seem to have gained her trust, which is very gratifying. 

There have been instances where I was asked to review and directly comment on other research lab colleagues' work who are involved in writing/research tasks. In many cases, I often felt like there was some kind of implicit resistance after a while (e.g. not meeting deadlines, not addressing my comments even if my supervisor wants them addressed, etc.). 

On paper, my colleagues often have a stronger research background than I (e.g. coming from research-oriented field or PhD student) while I'm MA level and coming from an arts background, which I feel might influence the situation. However, at any moment, if the supervisor does not agree with my comments, she can step in, as we usually work on shared files online. 

What could we do to ensure things go smoother and decrease the resistance?
If possible (given your knowledge of the subject, the regulations at your university, etc.), it might help if you get officially announced as these students (second-)advisor for their paper/thesis/... So the supervisor states that you are responsible for it, you are the one to contact with questions and (important!) your opinion will be important when deciding grades.
Right now, there is no reason for the others to listen to you, as you have no influence on their work/grades/... If the supervisor wants something, she will eventually say so and then they might do it, so why should they listen to you?
By making it clear that you are the one responsible for that and that the supervisor should only be contacted in case of severe problems, they will have motivation to listen to you, as you will be the one the professor asks in the end: "Well, I didn't read every last one of these 200 pages of the thesis and I hadn't as much contact with the student as you did, so what grade would you suggest?"

You don't even need to change anything in your working process, as you already said that the advisor reads your comments and only steps in if she disagrees, so you seem to already be responsible, you just don't have the power (over grades, etc.) yet to make them respect you.