Where to host lots of experiment data
I think figshare might be what you are looking for.

About figshare: 


  figshare is a repository where users can make  all of their research
  outputs available in a citable, shareable and discoverable manner


From their FAQ, What are the file size limits?


  Up to 5gb single file uploads 20gb of private space
  
  If these options do not meet your data needs do get in touch with us
  and we'll see what we can do.


Also, they offer unlimited public space, so I think they can cater your needs.