You cant make it look the same on different resolutions,
diferent browsers,
different OS,
most likely the movement is the page adjusting to the chosen measurements at the changed resolution
and regardless of resolution you cant even be certain what size window the page is opened in.

you can't make a paper layout the same on 8*11 and and 9*14 paper, in portrait and landscape either

but you can make it look good, by choosing a scalable layout.
float images in position and flow text around them.
set the most important paragraph/image/whatever in place, then let everything adjust around that