Would it be wrong of me to not want to be a shoulder to cry on constantly?
Why don't you want to be a shoulder to cry on? Does your friend cry to you all the time?
I don't know she just gets me to comfort her a lot by crying on my shoulders.
They just need someone who is there for them. You should be patient with them and just be there for them.
I am tired of it and I want to break up.
This sounds like they're more than just a friend towards you, and if that's the case then you need to be willing to listen when they want to vent. Sometimes being a shoulder to cry on can be annoying, but it is also pretty important to keep your relationship healthy.