Weighted Interval Merger

You are given a list of intervals, where each interval is represented as a triple (start, end, weight). The intervals may overlap. Your task is to merge all overlapping intervals. When two or more intervals overlap, the merged interval should have:

• A start equal to the minimum start among all overlapping intervals.
• An end equal to the maximum end among all overlapping intervals.
• A weight equal to the sum of weights of all overlapping intervals.

For example, given the intervals:

• (1, 4, 2)
• (3, 5, 3)
• (6, 8, 1)
• (7, 9, 4)

The merged intervals would be:

• (1, 5, 5) // because (1,4,2) and (3,5,3) overlap
• (6, 9, 5) // because (6,8,1) and (7,9,4) overlap

Write a function or method in your preferred programming language that accepts an array (or list) of intervals in the form of (start, end, weight) and returns a new array (or list) of non-overlapping intervals after merging them as described.

Consider edge cases and aim for an efficient solution considering both time and space complexity.

Good luck!