When I print on letterhead that is thicker, the alignment of the print is wrong.

Question

When printing on 20# white paper, the printer prints the file correctly.  When switching to a 24# letterhead, the printer prints lower on the paper, not in the proper area.

Answer 1

I am having the same issue.  My printer is an HP officejet pro 8600 plus.  When printing on letterhead paper the alignment is wrong.
My letterhead has a 1 1/2 inch header (the top 1 inch is blue).  The color goes to the edge of the paper.  The letterhead is the equivalent of #28 paper (heavier than copy paper).
When printing a letter I set it up to print 2 inches from the top of the paper.  (I normally do this by having the one inch preset margin in Word, and entering a few times until I am at the 2 inch mark on the side ruler. 
When I print a single copy of a document onto letterhead the printing starts at the 3 inches down on the sheet of paper.  (It is as if the printer cannot see the top 1 inch of blue  on the letterhead!!!) 
 If I print that same document on white paper the printing starts 2 inches down.
When I print multiple copies of the same document, all onto letterhead, the first one prints 3 inches down and the rest print 2 inches down.
I have tried:
Choosing a different paper type:  This did not work.  I tried thicker paper and custom paper but there was no change
Changing print source from auto to tray 1:  This made no change on a single document and caused EVERY document to print at three inches on multiple copies.
Changing to borderless printing:  No change
I tried a few other things - but nothing seems to work...