Included in my siddur as part of the sefirat haomer are the corresponding middat hayom for each day/week. They begin with chessed sh'b'chessed and progress through a series of middot - gevurah, tiferes, netzach, hod, yesod, malchut. From what I understand the order of the middot actually progresses in the opposite direction with Chessed being of a "higher" order and Malchut being the lowest rung. Assuming this is correct (and I do not have a source to prove that it is) why would we begin with the middah of chessed and progress "downward" instead of starting at malchut and proceed higher?
Omer is the time when we so-to-speak recreate ourselves in accordance with the Divine Will, so the creative process is a good represenation of what is spiritually happening during the time between Pesach and Shavuos.
The middos represent, in one sense, the stages of realization of that creative process. It starts with the highest forms (here, chessed) and proceeds to implementation until the lowest form of the implementation is complete (here, malchus).