I am struggling to define a log-likelihood based on an observed value of a quantity (data), the measured value based on a given model (model) and instead of using the errors (sigma) in the measurement of the observed quantity, I would like weighing them with a value which is a combination of errors and another measured parameter and it has reverse property, meaning it is higher for values with smaller errors mostly.

How could I substitute this value for each measurement instead of sigma in the likelihood function ?