Calculating weighted percentiles

That is a simpler approach.  I thought you needed a percentile calculation specifically, so tried to match that.  First thing to try for improved performance is to pull the filter evaluation out into a variable like this

WeightedPercentile_0.5 =
VAR pct50 =
    0.5 * SUM ( 'Balances'[WGT] )
RETURN
    MINX (
        FILTER (
            VALUES ( 'Balances'[INCOME] ),
            CALCULATE (
                SUM ( 'Balances'[WGT] ),
                'Balances'[INCOME] <= EARLIER ( 'Balances'[INCOME] )
            ) > pct50
        ),
        'Balances'[INCOME]
    )

That should help, but it still has a lot of calculation going on.  If you don't need it to be responsive to slicers, you could precalculate most of it as a calculated table.  You still could get different percentiles from that table, but the heavy calculating would already be done at refresh.

If this works for you, please mark it as the solution.  Kudos are appreciated too.  Please let me know if not.

Regards,

Pat