Weighted Interval Merger

Your task is to write a function that takes a list of intervals, where each interval is represented as a list of three integers: [start, end, weight]. The function should merge all overlapping intervals and combine their weights.

Two intervals are considered overlapping if they share at least one common point (i.e., for intervals A = [a_start, a_end, a_weight] and B = [b_start, b_end, b_weight], they overlap if a_start <= b_end and b_start <= a_end). When merging overlapping intervals:

• The merged interval's start should be the minimum of the overlapping intervals' start values.
• The merged interval's end should be the maximum of the overlapping intervals' end values.
• The merged interval's weight should be the sum of the weights of the overlapping intervals.

The function should return the merged intervals as a list, with each interval represented as [merged_start, merged_end, total_weight]. Make sure the resulting intervals are sorted by their start time.

Example:

Input: [[1, 3, 2], [2, 6, 3], [8, 10, 1], [15, 18, 4]]

Possible Output: [[1, 6, 5], [8, 10, 1], [15, 18, 4]]

If no intervals overlap, the function should return the original intervals sorted by start time. You can assume that for every interval, start is less than or equal to end.