weighted average date

This measure expression gets your expected result in a table visual with your Client column.  Please check it with your real data.  Replace "weighted" with your actual table name.

Weighted Date =
VAR mindate =
    MIN ( Weighted[Payment date] )
VAR summary =
    ADDCOLUMNS (
        SUMMARIZE (
            Weighted,
            Weighted[Payment date],
            Weighted[Amount]
        ),
        "@days",
            DATEDIFF (
                mindate,
                Weighted[Payment date],
                DAY
            )
    )
VAR wavg =
    ROUND (
        SUMX (
            summary,
            Weighted[Amount] * [@days]
        )
            / SUMX (
                summary,
                Weighted[Amount]
            ),
        0
    )
RETURN
    mindate + wavg - 1

Regards,

Pat