The Weight, according to Louis:
Weight tells SAM how important a song is, while Weight balance tells SAM how much this song has played relative to other songs.
It is recommended to always reset your weight balance after adding a lot of new songs.
If you want to keep a constant relationship between songs, fix the weights as indicated above. My mix is based on chart position so I use weight to keep things in check, as it were. I periodically run a SQL UPDATE to adjust the weight of groups of songs then use Adjust Weight Balance to get everybody back on an even keel.