>In IE, it fires multiple times per 1 pixel. In other browser, it fires only once per pixel. Based on what I read, this just depends on how the browser's manufacturers has their view on on the resize should work.

http://www.quirksmode.org/dom/events/resize.html
states:

Amount of events
=============

But how many events fire, and when? On Windows 7 and Mac 10.6 all browsers fire many events during the resize action, except Opera Mac, which also fires many events, but only when the resize action has ended.

Windows XP
----------------
On Windows XP, if you switch “Show window contents while dragging” off, all browsers fire one resize event at the end of the resize (except for IE 5.5 and 6, which fire two).
  In IE, Safari, and Chrome many resize events fire as long as the user continues resizing the window.
  Opera uses as many resize events, but fires them all at the end of the resizing.
  Firefox fires one resize event at the end of the resizing.

It looks like you can't count on a pixel-by-pixel resize() firing.
One way could be to store .minWidth and .maxWidth somewhere in the DOM and test in resize() if dimensions are larger and smaller, then get back to min/max.

should work on end-of-resize firing, maybe not on pixel-by-pixel resize() firing.