I am trying to sort elements in multiple lists into buckets with weighted data. I can do the single-list case based on a previous question. Specifically, the code under Update in the first answer.

data = {1, 2, 3, 4, 5, 6, 7, 10};
bins = {0, 2, 4, 6, 8, 10};
weights = {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 1.0};

With[{ranges = Partition[bins, 2, 1]}, 
 Total@Pick[weights, 
     BitXor[UnitStep[Subtract[data, #1]], 
      UnitStep[Subtract[data, #2]]], 1] & @@@ ranges]

which gives the following output: {0.1, 0.5, 0.9, 1.3, 0}

Now, I'm trying to generalise to the following input:

data = {{1, 2, 3, 4, 5, 6, 7, 10}, {3, 5, 6}};
bins = {0, 2, 4, 6, 8, 10};
weights = {{0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 1.0}, {0.4, 0.6, 0.5}};

I can't use the same code, because Pick does not treat each list sequentially. However, I can get the desired result using this code (where I make it take the first and second list separately:

With[{ranges = Partition[bins, 2, 1]}, 
 Total@Pick[weights[[1]], 
     BitXor[UnitStep[Subtract[data, #1]], 
       UnitStep[Subtract[data, #2]]][[1]], 1] & @@@ ranges]

With[{ranges = Partition[bins, 2, 1]}, 
 Total@Pick[weights[[2]], 
     BitXor[UnitStep[Subtract[data, #1]], 
       UnitStep[Subtract[data, #2]]][[2]], 1] & @@@ ranges]

{0.1, 0.5, 0.9, 1.3, 0} {0, 0.4, 0.6, 0.5, 0}

But I want to generalise to a large number of lists now. I tried a loop but when i generalise to a loop it does not work:

For[i = 1, 2, i++,
 With[{ranges = Partition[bins, 2, 1]}, 
  Total@Pick[weights[[i]], 
      BitXor[UnitStep[Subtract[data, #1]], 
        UnitStep[Subtract[data, #2]]][[i]], 1] & @@@ ranges]
 ]

How can I generalise it cleanly?