Thanks for the details.
So indeed for that particular net of conv + relu + l1, you get this result (i didn’t dive into the calculation but that sounds plausible).

So the question is, how loss has contributed to change in weight?

The actual value of the loss does not in this case. If you look at the overall function you wrote, it is actually linear at that point with slope x. So the only thing that will influence in which direction you should move is going to be x.
The simplest analogy here is a 1D identity function: whatever the current point, the gradient is always 1 (the slope x in your example). So you should move to lower values. The actual value of the function is not changing anything.
You can try to do the same computation with a l2 loss (that is not linear) and you will see that the value of the loss will start appearing in the final result.