SQLServer In-Memory database and log file size unexpected increase
OK, I didn't find a clear explanation, but found how to fix that.

It was because file used to store in-memory objects was full and could not allocate more space. So no more checkpoints, and logs and growing more and more. This is happening even though there is no in-memory objects in the database (and therefore no reason for the data file to grow). 

Allowing file to grow more is not working, you need to add another file to your filegroup.

So, knowing that, it's easy to fix.


add another file into the filegroup for in-memory 
checkpoint (or, if you can afford it, restart SQLServer service)
shrink log file to a more reasonable size


Conclusion of the story : carefully monitoring data size is even more important with in-memory.