Yes the Lamy 2000 is a bit heavy, for me.
Mine weighed approx 25 grams.
My standard writing pens are down at about 15 grams (Parker 51, 45 and Classic)
> It seems the pen is always being pushed onto the paper and my hand has to make the effort to separate it from the paper. <
Is this on the down-stroke, up-stroke or side-stroke?
Some times stroke direction causes you to change your pen pressure.
Check that you are not rotating the pen.
If you rotate the pen and this happens on the up-stroke or side-stroke, then the corner of the nib will dig into the paper. Or once you are off the sweet spot of the nib, you get less ink flow and thus less ink lubrication and more drag.
BTW it is very easy to rotate the pen without being aware of it. I did it often with the L2000, and I do it often with my Parker 51. This is simply because you do not have a good visual reference on the nib.
Where do you grip the pen?
I hold my 2000 with my fingers just above the section and below the ears that hold on the cap, and my thumb above the ears. The balance feels fine there.
Where you hold the pen with your fingers and where it rests on your hand affects how the balance feels. If you have big hands, the balance point will likely be more towards your finger than just below where it rests on your hand.
I have a small hand, so the opposite happens to me. Many pens feel back heavy when posted.