How to increase the weight when it comes to outlier detection Let's say we have feature A, B, C, D, E to represent one observation in an outlier detection model. We are using scikit-learn outlier detection in our case.

AFAIK, if we normalize all the features, they are as equally important as others.

What if I want to make B very important, e.g. if A, C, D, E increase 20%, the observation might still be considered as normal case while B increases 10%, the observation needs to be marked as an outlier. 

Is there any way to increase or decrease features' weight in outlier detection model?
Please look at my answer at Identfying spikes in data
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A general method could be to calculate a (moving) average and standard deviation.
Outliers are points that differ more than 3 times the standard deviation.

In your case, B will probably have a standard deviation of 3%, because 10% is considered an outlier. For A, C, D, E, the standard deviation may be 7%, because 20% is not considered an outlier.

Relative importance does not make something an outlier. A large deviation does.