What an interesting topic guys! 
One of the tropes that makes me go "huh?" is "the small kid who is extremely powerful" with no reason at all, just to make him/her look cute or something. And its even worse when you have a well trained adult with him who has spend years learning what that child could do just by blinking.
I also hate "I'm a girl so I must be the healer"
I know they want the MC to do most of the job, but they could also fight together.
In romance I don't like the one that makes one of the characters act like some kind of child while the other is so composed and brave, sometimes its so extreme that it actually feels like some kind of abuse to an underage person
in BL tends to be more common, with a guy acting like a 5 year old while the other looks like a full employee (while being actually a high schooler).