First, Moore's law is only an empirical observation. Sooner or later, the laws of physics will mean that it is no longer possible to keep increase uniprocessor speed. Moore's law is not a useful predictor of the future in the medium to long term, and possibly not even in the short term.
Second, strongly and weakly typed languages are EQUALLY affected by Moores law.
Third, Moore's law is about uniprocessors. We're well into a world where increases in raw computing power are coming through multi-processing, but there aren't the software tools (e.g. languages) around yet that help the average Joe programmer to write programs that take advantage of multi-processing. However, functional languages offer more promise in this area than procedural ones.
Fourth, I think you are really comparing statically typed versus dynamically typed languages. (The terms "strongly typed" and "weakly typed" have become so confused due to conflicting definitions that they are no longer meaningful.)
I guess your argument is that Moore's law means that efficiency matters less, so we can "get away with" using less efficient computation paradigms; e.g. dynamically typed languages. (And if we are talking about interactive tasks, the computer only needs to keep up with the user's speed of asking for things and mentally processing the answers.)
The flip side of that argument is that people are wanting their computers to do more compute intensive things; e.g. each generation of computer games requires more power to do the graphics. Online business wants to do more things (e.g. serve more web requests) faster with hardware that is cheaper to run. In short, there are lots of situations where efficiency does matter, and this will always be the case.
So what you find is that in places where speeds is important, we tend to use efficient computing techniques, and where it is unimportant we use techniques that minimize software development and maintenance costs.