Guidelines in selecting weight in weighted squared error loss function

Question

I am new to loss functions in Bayesian analysis and from what I understand are:

1. Squared error loss function - the estimator will be the posterior mean.
2. Absolute error loss function - the estimator will be the posterior median.

I came across another loss function named as Weighted Squared Error Loss function which introduces a weight to the squared error loss function. I also read that the weight will affect the estimated parameter value.

Is there any guidelines to how to develop the weight or how to select the form of the weight (fraction or exponential or log, etc.)?