The web UI only supports uploads smaller than 2^32 bytes (4 GigaBytes). I believe this is a javascript limitation.
If you need to transfer many or large files consider using gsutil:
- GSUtil uploads and downloads any size file.
- GSUtil resumes uploads and resumes downloads that fail part way through.
- GSUtil calculates the MD5 checksum to verify the contents of each file transferred correctly.
- GSUtil can upload and download many files at the same time.
gsutil -m cp /path/to/*thousands-of-files* gs://my-bucket/*