Searching in the issue tracker, looks like this feature is in scope if I understand correctly #20522 (comment).

cc @snath-xoc and @jeremiedbb for an informed opinion, since they have been working on sample weights support recently.

@antipisa would you be interested in contributing a PR? There is already a common test named check_sample_weight_equivalence_on_dense_data that should be triggered as soon as you add the sample_weight kwarg to fit. Once this is done, the following command should pick it up:

pytest -k "check_sample_weight_equivalence and QuantileTransformer" sklearn/tests/test_common.py -v  -s 

You might want to adjust some non-default parameter values for that check in PER_ESTIMATOR_CHECK_PARAMS in sklearn/utils/_test_common/instance_generator.py.

Note that when subsampling is enabled, we need to follow a similar strategy as implemented in KBinsDiscretizer. At the time of writing, the code for KBinsDiscretizer in main is still half broken, but there is a fix that is almost ready to be merged: #29907. You can take a look at this PR for inspiration.

We are working on tooling to help test the case where the estimator's fit is stochastic (depends on random_state which is the case when subsampling is enabled). You can track the latest progress here: #16298 (comment)

I will take this!