Weighted Interval Merging

You are given a list of events. Each event is represented as a triple of positive integers: (start, end, weight), where start < end. The list may come in an arbitrary order.

When events overlap, the event with the higher weight takes precedence during the overlapping period. If two overlapping events have the same weight, the event that starts earlier takes precedence.

Your task is to write a function that processes this list and returns a new list of non-overlapping intervals. Each interval in the output should be represented as (start, end, weight), indicating that the interval [start, end) is covered by the event with the specified weight.

The function should:

• Split intervals when the covering event changes due to overlapping events with higher weight.
• Return the list of intervals sorted by their start time.
• Handle an empty input list by returning an empty list.

For example, given the following events:

• (1, 5, 10)
• (3, 7, 15)
• (6, 9, 5)

The expected output would be something like:

• (1, 3, 10) // Only the first event covers this interval
• (3, 7, 15) // The second event (with higher weight) covers this interval despite the overlap
• (7, 9, 5) // After the higher weighted event ends, the third event covers the remaining interval

Note: The above example is illustrative. Your solution should work for any valid list of events.

Your implementation can be in any programming language of your choice.