How to fix an artifact affecting a bevel modifier This is me yet again.

I am trying to work non destructively with the use of bevel modifier. I managed to bevel only by weight and adjust the weight of desired edges. 

However, now when I try to place loopcuts for further knife projection of other planes, I get this weird artifact on my bevel modifier. Now, I know I could apply the bevel modifier and then do it, but I am trying to see if there is a way to do it non-destructively.

Ideas I have so far: 


Block out the main bits and worry about the modifiers only in the end, but I don't see how that will improve the situation.
The artefacts occur because you have a beveled edge adjacent to an unbeveled one. You are not creating topology at the bottom of your mesh so you have an area where faces with different number of vertices meet. You could give all effected edges a tiny bit of bevel, instead of none, that would mask the problem. Otherwise it's going to take manual refinement.