Calculate a weighted average of a score, with increasing weights with respect to updateness of the month considered [SQL]

Question

I'm having problems to calculate the weighted average of a score, considering a windows of three months.
I would assign weight = 1 for the current row, weight of 0.5 for the previous month and weight of 0.33 for the last month of the time window. Then repeat the same logic for the second line which will have weight 1 the 2nd of 0.5 and so on..

I'm triyng with this query but it doesn't work like I would:

SELECT 
    anno, 
    mese, 
    id_lince, 
    score_s1_norm,
    SUM(score_s1_norm * weight) OVER (PARTITION BY id_lince, anno ORDER BY anno DESC, mese DESC 
                                      ROWS BETWEEN 2 PRECEDING AND CURRENT ROW) / 
    SUM(weight) OVER (PARTITION BY id_lince, anno ORDER BY anno DESC, mese DESC 
                     ROWS BETWEEN 2 PRECEDING AND CURRENT ROW) AS weighted_avg
FROM (
    SELECT 
        anno, 
        mese, 
        id_lince, 
        score_s1_norm,
        CASE 
            WHEN ROW_NUMBER() OVER (PARTITION BY id_lince, anno ORDER BY anno DESC, mese DESC) = 1 THEN 1
            WHEN ROW_NUMBER() OVER (PARTITION BY id_lince, anno ORDER BY anno DESC, mese DESC) = 2 THEN 0.5
            WHEN ROW_NUMBER() OVER (PARTITION BY id_lince, anno ORDER BY anno DESC, mese DESC) = 3 THEN 0.33
        END AS weight
    FROM lab.S1_cg14 d
) AS weighted_data
ORDER BY id_lince, anno DESC, mese DESC;

(https://i.stack.imgur.com/78xwT.png)

For example, the Weighted-AVG for the first line should be: SUM(Score * Weight)/SUM(Weight) (1 * 79.4 + 0.5 * 94.4 + 0.33 * 95.4) / (1 * 0.5 + 0.33) = 0.906

Thanks in advance to all who can help me