I have written Huge JSON viewer based on JSON.NET, one of the fastest JSON frameworks. It matches the requirements as follows:

• open decently large files: it can open the 1.44 GB example file without crashing in ~ 2:45 minutes on my machine (Intel Core i7, 16 GB RAM, SSD). To do that, the OS must be 64 bit. A progress bar is shown
• has a decently responsive UI: I use a commercial tree view from DevExpress which I hope is optimized very well.
• can collapse/expand a given level: it is a full tree view and can expand/collapse any nodes. It has a feature to expand to a given level
• works off-line: it's a Windows desktop application. Needs .NET
• provide some statistics on the JSON content: some. Can definitely be improved.
• tabs: yes.
• gratis: yes. MIT license, but closed source.
• displays the filename somewhere: yes, in the tab

The only thing it can definitely not (but was optional):

• "can edit JSON data"

Additional features:

• search capability
• performance warning when memory swapping to disk is expected

System requirements:

• Windows 7 SP1 or higher, x64 bit recommended
• Physical RAM roughly 7 times the file size to be opened
• .NET 4.5

Watch out the list of known issues until it's out of beta phase.

Screenshots:

Download (including portable version): https://github.com/WelliSolutions/HugeJsonViewer#releases

If you're using Mac, try Hex Fiend. Loads large files super fast. Just disable the hex view and you'll get a regular-ish editor.