Sync intentionally doesn't allow you to see your data on the web: it's encrypted. If you could view it through a webpage, it could be stolen or subpoenaed, and we're not willing to take that risk with your passwords and history.
If you want to see what Sync is doing, you can add the Sync icon to the Add-on toolbar. If you really want to see what it's doing, turn on logging and look in about:sync-log!
Speaking of private data and encryption, do you know which FF file is responsible for History data? I know the Bookmarks json file but I'm looking to keep my history file as a backup too (which I believe FF doesn't backup like it does bookmarks). I hope it isn't places.sqlite file because it gets ridiculously huge even after you wipe your data clean.
I wish to rely on my own backup system for both bookmarks and history data as both of them are important on continuous basis and both of them should be user's own responsibility (unlike what delicious or many other bookmarks syncing services may tell you).
Yes, places.sqlite stores the history. The reason it grows by large increments (and does not shrink to very small sizes) is to prevent file fragmentation, which can have a big effect on the speed of the browser.
And, I'd assume that even if deleting history doesn't shrink places.squlite, someone who wants to create a backup will be compressing it. And a mostly empty but large file should compress to a tiny file, right?
Okay, I'll give these two suggestions a try. Sync worked the first time for me but then it just stopped. It no longer brings my stuff over to new profile/install, so I was curious to see if my data is even there or not (which is not a big deal as I have backup and I was just testing). It would help to have an activity monitor somewhere or a way to check the percentage of syncing done.
If you want to see what Sync is doing, you can add the Sync icon to the Add-on toolbar. If you really want to see what it's doing, turn on logging and look in about:sync-log!