Euclidean Distance with Weighted Values

I am currently dealing with a dataset which consists of about 2700 points stochastically placed in a study area of about 650,000 sqKm. I am trying to create a distance raster for these points, which I have been able to do using Euclidean Distance tool, but I would like this distance raster to also be affected by the class of point being evaluated. For example the points range in value from 6 to 10. Therefore I would like the raster to be affected by these values. So for points with a high value I would like the distance value to be lower as to positively affect a Cost raster and eventual least cost pathway.

I know that this is a little vague, I apologize it is because I do not know what this concept would be called. Any insight would be extremely helpful.