There is no overall repository size limitation in Assembla.
However, due to general GIT design specifics, we apply strict maximum file size limit, to prevent one repository from generating excessive load and affecting other customers on our servers.
We place strict maximum file size limit: 400MB.
GIT is not very good solution if you need to work with large binary files. You may consider using LFS or switching to Perforce if you want to commit large binary files.
You may also be interested in Assembla's Private Installation on dedicated hardware, which is free of the limitation mentioned above.