I perfer to look at these situations differently than most people do I assume. As I've mentioned in a previous post I prefer a strategy where I understand my range, where I am at in my range with my current hand(top 10%-20%,30%, etc) and ask myself questions like "how often do I need to call to make my opponent indifferent to bluffing". There is some important information like positions, etc that was left out of the OP. For now I am going to assume that OP was in the blinds since he is 3 betting out of position. It is either that or OP open limped his KQ preflop? Without knowing the villians position I can really only take a guess. So for my answer I am going to assume hero is in the BB and villian is something like MP1. Also, for my type of answer your 3 betting range is very important in order to determine the correct action. Just to make life easier I'll use the predefined ranges in equilab for a bb 3bet against MP villian but in a real life situation I would highly recommend having a more balanced range than what they show.
Assuming a 3 betting range from the BB against a MP open raise of:
99+, ATs+, KQs, AJo+
The next step is to rank the range from best possible hand to worst possible hand as it relates to the flop. So something like this:
Flop: KJ9
KK, JJ, 99, AA, AKs, AKo, KQs, QQ, AJs, AJo, TT, AQs, AQo, ATs
Now we're looking at a 100bb bet into a 50bb pot. The formula I use for determining how wide I should be calling out of my range which beats a bluff is: 1/(1+(bet/pot)) which in our case comes out to 33%. So now we look at our hands that beat a bluff which we could debate where the actual cut-off but just to make life easier I'll say TT is our bottom bluff catcher. That gives us 11 hands in the range above to choose from. We need to call with 3.6 hands starting from the top of our range. This means we should be calling with KK, JJ, 99 and AA just over half of the time.
The result can change a great deal based on your 3 betting range. This answer assumes the 3 betting range I mentioned. If we were to use something more like what snowie suggests in this spot we would use the following range:
So that gives us a potential 3 betting range of: 99+, 66, ATs+, KQs, QJs, JTs, T9s, 98s, 87s, 42s, 43s, AQo+, A4o, A2o
A good deal of that range is only going to be raised a realtively small percentage of the time. Also, if you have noticed neither 3 betting range has had KQo in it.
So lets do the same sort of ranking as above:
KK, JJ, 99, AA, AKs, AKo, KQs, QQ, AJs, AJo, QJs, JTs, TT, T9s, 98s, 66, AQs, AQo, ATs, A4o, A2o, 87s.
In this example, I'll use 98s as our bottom of our range which beats a bluff. So using the same logic as before we have 15x bluff beating hands and need to be calling with 33% of them to make our opponent indifferent to bluffing. So with this range you would be calling about 5x hands so KK, JJ, 99, AA and AKs like 95% of the time.
KQo was not in either range and KQs was a pretty solid fold in both ranges.