01 Knapsack with selection of items with minimum total weight
Sure.  It's easy to take any algorithm to solve the ordinary knapsack problem, and apply it to your problem.  In the ordinary knapsack problem, we specify an upper bound on the weight.  Once we find the maximum value achievable with that weight, next we'll try to see if we can reduce its weight further.  Do this by solving a new version of the knapsack problem, the same as the original, except the maximum weight has been reduced.  See how far you can reduce the maximum weight while still achieving the same value.  You can use binary search for that.