Knapsack dynamic programming complexity issue for $W=1$, is it $O(n)$?
The running time is $O(nW)$ if all weights are integers. This is because the dynamic programming table is indexed by possible weights of subsets. If all weights are integers, then since we are only interested in subsets whose sum of weights is at most $W$, there are only $W+1$ weights of subsets that could possibly interest us. This is where the $W$ factor in the running time is coming from.

Dividing all weights by $W$ accomplishes exactly nothing. You haven't changed the problem, so the required time for solving it is remains exactly the same.