I tried this with a small (about 250' N-S) project I did recently:
I had 4-minute RTN observations on points 1 (just to the left of 4), 2 and 3. I weighted the RTN coordinates at 1.00' in all 3 dimensions. Here are the results:
Is this what you mean by weighting the coordinates?
I must be doing something wrong because it is exceeding positional tolerance significantly.