Get layer Height when the Width hit a specific value

You would not necessarily base this on time at all. Something like this might suffice:

threshold = effect("EndLimit WIDTH")("Slider");
wid =Math.round(thisLayer.sourceRectAtTime(time).width);
hei=0;
snap=false;

while (time < thisComp.duration){
if (wid < threshold){
hei++;
break;
}else if (wid >= threshold){
snap = true;
}

if (! snap){
out=value[1];
}else{
out=hei;
}

Haven't checked this inside AE, but I hope you get the gist.

Mylenium

You may need to insert a break or continue in there somewhere, wrapped into a conditional. Hard to tell without seeing the code you actually used. Dan's audio trigger example might give you an idea, as it essentially covers your scenario, just based on audio:

http://www.motionscript.com/design-guide/audio-trigger.html

Mylenium

For the super exact version working with any transforms and effects would have to run a while() loop that keeps on checking whether this threshold is met and then trigger a sampleImage() based on the time derived by the previous loop. Other than that of course you can always calculate this using a bunch of linear() functions, assuming there is nothing else going on. You need one function to correlate the input size or percentage value to the comp width, the other to compare the result of the first function to your scale animation and calculate the horizontal size.

Mylenium