To be honest I find "ever" a little weird with "favourite", but although I might not use that combination myself, some people certainly do.
You will see/hear "ever" used a lot with superlatives, especially "best" and worst":
That was the best night ever.
That was my worst presentation ever.
As Ahmed says, "ever" gets strong word stress in these kinds of sentences. You can also move "ever" to be directly after the superlative ("fastest ever time", for example) in which case we don't stress "ever" quite as much.