Hi,
First of all, it is usually recommended to normalize the input, so maybe you could try to change the range of the input from (1-256) to (-1, 1). I think this might help.
If you want know how much does an input affect to the output, maybe you could try monitoring the gradient vector’s magnitude. I mean the gradient with respect to the input label, not with respect to the weights. If the gradient is very small, it might mean that the input makes small difference on the output.
Ideally, the model should be able to learn the importance of the label in the input, but if you want to “artificially” force that, maybe you could try repeating the label a bunch of times in the input?
Hope this helps