A Barlow lens will have a different magnification factor at different distances from the lens--the farther the distance, the higher the magnification.
Eyepieces don't all have their focal planes at the same point within the barrel--they vary from a focal plane as low as near the bottom of the eyepiece to well above the "shoulder" the eyepiece
sits on when it is inserted.
As a result, every eyepiece will have a slightly different magnification when used in a Barlow, and you can even change that by simply sliding the eyepiece 1/4" out of the Barlow and tightening
it down at that point.
Many, if not most, Barlows have their magnifications specified to be when the focal plane of the eyepiece happens to coincide with the opening of the Barlow.
Most eyepieces don't have their focal planes exactly there, so magnifications will vary. And magnification factors on Barlows are often rounded off: 2x claimed could easily be 2.1x actual.
You can easily discover the magnification factor of the Barlow without measuring anything other than to take a timing of the passage of a star from edge to edge across the center of the field of the eyepiece
both with and without the Barlow. It doesn't even matter where in the sky the star is, though your timing will be shorter if the star is near the celestial equator, if time is a factor.
The relationship is this:
Timing without Barlow ÷ Timing with barlow = magnification of the Barlow with that eyepiece. Do a good job on the timing, and you can get the magnification factor to 2 decimal digit accuracy.