Non-confidential student suppport letter for a teaching award
I can't see into the minds of the judges responsible for the award, but such letters might well be discounted. The problem is the possibility that the students were actually writing to solicit favors from you in the future - trying to "get on your good side". Actually, it is the perception that they might be trying to get some future favor. 

You might suggest to the writers that they send letters directly. 

In any case, the direct answer to whether confidential letters might hold more weight is yes, they might. 

But if there are a combination of letters sent confidentially and not and they are consistent, then I doubt it would be a problem. 

But IANAMR (I am nor a mind reader).