I'd draw the table more like this

  Metric       Weight  Percent   Score  Weighted_score
Leadership       40      40%       2      0.8
Punctuality      20      20%       2      0.4
Cleanliness      30      30%       2      0.6
Responsiveness   10      10%       2      0.2
Total           100     100%              2.0
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Then remove one item and you don't have to change any weights, just calculate the new percentages and weighted scores:

  Metric       Weight  Percent   Score  Weighted_score
Leadership       40     50%        2      1.0
Punctuality      --     --%       N/A     ---
Cleanliness      30     37.5%      2      0.75
Responsiveness   10     12.5%      2      0.25
    Total        80    100%               2.0
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A percentage is just a type of weight but weights don't have to add up to 100 while percentages do. So dealing in weights that aren't (necessarily) percentages is more flexible and easier to understand when you have a problem like this.