you know little of economics. the ability to use economics as a diplomatic tool is about size, which almost 100% dictates influence. biggest is definitely best.
the weak dollar indicates decreased demand, but it had to happen for several reasons. the relative strength of our dollar is huge in BOP math, otherwise it dictates how your money spends abroad or on imports. being the biggest outlet for world goods means that most int'l companies have to maintain their dollar denominated pricing so we don't feel the weaker dollar, while our domestic products become massively more attractive overseas.