If your tweeters are being over driven and the mid/subs are weak, that's not a power issue with the amp, unless you're noticing major clipping. Something else, like a blown crossover in the speakers or incorrect crossover settings on the receiver is the issue.
The amp only sends one power source to a speaker, not separate ones for each driver(unless you're talking about biamping and such). If your amp does 100 watts a channel, that's 100 watts total for everything contained in a single speaker. How the power gets divided up once it reaches the speaker depends on the speaker's crossover(if there's a passive crossover in the speaker, which there usually is) sending different frequencies and power amounts to each driver.
If the tweeters seem way too loud compared to the rest of the speaker it means the mid/subs are blown, the crossover in the speakers have been damaged somehow which is preventing the proper signal from reaching the drivers, or your receiver's crossover is set really really high so that most of the low frequencies are going straight to the sub which means your woofers in your speakers wouldn't be doing very much work at all.
Amp ratings are for max clean power(although how they come up with the numbers usually involves lots of tricks to overstate the true power). Speakers power ratings are generally max power handling ability. 200watt speakers dont require 200 watt amps, that just means they can handle that much current without blowing. Your receiver should be able to handle the speakers just fine.