I am thinking that you are saying both left side and right side should have equal total weight.

Then:-

You can approach this question using dynamic programming.

The approach currently coming in my mind is dp[i][wt1][wt2] (bool variable)

it means is it possible upto ith weight that left side have wt1 and right side is wt2.

Now we have three option that

- dont put this weight on left and right side :-

dp[i][j][k] |= dp[i-1][j][k]
- put this on left side

dp[i][j][k] |= dp[i-1][j-wt[i]][k]
- put this on right side

dp[i][j][k] |= dp[i-1][j][k-wt[i]]

Then answer will be for which maximum w dp[n-1] [w ][w] is true.