Actually they would be inversely related. Less valuable dollars will buy less bit coin. Less valuable bit coin would mean you can get more of them for a dollar.
If you live in Canada and I live in Mexico and our exchange rate is 1:1, but I can buy milk for $10 while you need to pay $13 for milk, the Canadian currency has less purchasing power. Also assuming the milk is the same brand, same amount, same quality, etc.
Weaker dollars may not be a bad thing, but if the purchasing power falls, then that will be hopefully reflected in the Bitcoin price. It will go up in sync, or whatever the investors feel like doing.