Argument strength is how much the evidence favors your hypothesis (the proportion of heads to tails when you're checking if a coin is weighted).

Argument weight is the number of tests that you've done. (Have you flipped the coin three times, or one hundred?)

People treat 5 tests, all heads as better evidence of a weighted coin than 1000 tests, 55% heads. The latter is actually more indicitive of a weighted coin (assuming sane priors).

Sorry, I should have made this more clear. I'll edit the post.