scikit-learn: Inconsistent behaviour of decision trees with equal weights of samples

It seems to me the structure of trees shouldn`t change after multiplying the weights of all samples by some constant, but I get different results.

Example

from sklearn.tree import DecisionTreeClassifier

X = [[1, 0], [1, 2], [1, 1], [0, 3]]
y = [False, False, False, True]

for w in [1., 0.1, 0.01, 0.001, 0.0001]:
    model = DecisionTreeClassifier(random_state=0, class_weight={False: w, True: w})
    model.fit(X, y)
    print(w, model.tree_.threshold, model.tree_.feature)

Results:

1.0 [ 2.5 -2.  -2. ] [ 1 -2 -2]
0.1 [ 2.5 -2.  -2. ] [ 1 -2 -2]
0.01 [ 0.5 -2.  -2. ] [ 0 -2 -2]
0.001 [ 2.5 -2.  -2. ] [ 1 -2 -2]
0.0001 [ 2.5 -2.  -2. ] [ 1 -2 -2]

The same problem with w = 0.01 also occurs with DecisionTreeRegressor, when the weights passed through the fit method.

Interestingly, the problem disappears in this example with np.float32(w) instead of w, but still appears in different situations.

Versions: Scikit-Learn 0.17.1, NumPy 1.11.1, SciPy 0.17.1, Python 3.5.2, Windows 10.