How to find splits in data so that each split has equal weighting according to function f
A classic optimization problem! You can use Linear Programming/Optimization to find a good split. Every of the n samples s $\in S$ has weight f(s) and we want to divide them into m folds. You can use a trick to linearize the L1 objective or you can use Quadratic Programming for a L2 objective function. The Quadratic Programming model is easier to define in this case. Let's define $x_{ij}$ as a binary decision to put sample i in fold j and $\mu$ is the ideal, mean weight per fold. Then this is our objective function:

min $\sum_{j=1}^m(\sum_{i=1}^nx_{ij}f(i)-\mu)^2$

Under the following constraints:

$\sum_{j=1}^mx_{ij}=1$ for all $i\in \{1..n\}$ to ensure exactly one assignment per sample

$x_{ij} \in \{0, 1\}$ to turn it into binary decision varibales

Depending on the size of your dataset and the solver you use this can be a heavy optimization, but there are a lot of greedy heuristics that will get you close fairly fast.