I've experimented with the whole button thing and it really doesn't matter. If your Tama is heavier, then it may win more, although there are variations in how many points you get based on the weight. I believe it goes something like this:
10-49 lbs: 5p, 40p, 80p, 120p, etc.
50-? lbs: 5p, 30p, 60p, 90p, etc.