Low power amps and speaker damage?

As I understand it tweeter have less power handling capacity than mids or woofers.  If an amplifier clips it can produce a square wave type signal with a large amount of higher harmonic content that would normally never be present in music.  The key factor is whether the amplifier can exceed the tweeter's power handling capabilities.  If you clip a 70 watt amplifier for a significant amount of time it's far more likely to damage a typical tweeter than a 5 watt amplifier.

Historically its common for low power amps to damage speakers particularly tweeters when they hard clip and distort.

Tube amps typically soft clip and are less likely to cause damage when clipping to speakers because they distort differently. Read up on clipping and differences between hard and soft clipping for more.

My personal experience is that advances in amp and speaker design over the years makes this less of an issue than in the past, but still something to be aware of and avoid. Clipping is public enemy #1 to good sound....it is distortion and can easily occur anytime to the detriment of sound quality even if no physical damage done. So always better safe than sorry when it comes to having sufficient power to drive speakers to desired levels with minimal distortion. 

When at clipping basically the tweeter sees a peak level for an extended period of time. No time for voice coil to cool. Have you ever seen a tweeter on fire? 
It does not matter if the amp is big or small, you can damage speakers either way.
A small amp let's say 5w most likely will not do any harm when clips as its peak output would be much less than the continuous power handling of the tweeter.
A 30w amp has more chances to destroy tweeters.

MC 
Mine goes to 11.
Nyah nyah.
What Erik said.
iPad ain’t got enough power for destruction.
Doh.
The only tweeter I ever fried was 18 watts, AB SS with a goofy broad at the controls.

I learned the hard way  early on frying several Heil AMT tweets with a 40 watt integrated amp many years ago.   Never again.