Is it possible to have differential weights as per input importance for a Neural Network
Yes! It is totally possible, generally weights are never same, they differ for different inputs.This is the first reason why they are called weights, as they associate weight to every input.

Preparing neural network parameters (weights and bias) using TensorFlow Variables in python:(assuming you have 3 inputs and want to assign them with .3,.1 and .8 weight respectively.)

weights = tensorflow.Variable(initial_value=[[.3],[.1],[.8]],dtype=tensorflow.float32)  
bias = tensorflow.Variable(initial_value=[[1]], dtype=tensorflow.float32) 


Happy to answer.