This is the truncation (or weight-reduction) algorithm as it now stands.

#!/usr/bin/env perl
use v5.36; # implies warnings
no warnings q/experimental::for_list/;
no warnings q/experimental::builtin/;
use builtin    qw/indexed/;
use List::Util qw/sum/;

my $target_weight = shift // die 'need target_weight';

my @weights = ( 20, 3, 25, 10, 3, 24, 25 );

say "Before:\n" . display( \@weights, $target_weight );
shrink( \@weights, $target_weight );
say "After:\n" . display( \@weights, $target_weight );
die if sum(@weights) != $target_weight;

sub shrink ( $bags, $target_weight ) {
    my $curr_weight = sum @$bags;
    return if ( $curr_weight <= $target_weight ); # no shrink req'd
    my @refs = sort { ${$b} <=> ${$a} } map \$_, @$bags;
  BAG:
    for my ($i, $ref) ( indexed @refs ) {
        my $next_wt = $i < $#refs ?
            ${$refs[$i+1]} : 0;
        my $drop = $$ref - $next_wt;
        my $lowered_weight = $curr_weight - $drop * ( $i + 1 );
        if ( $lowered_weight >= $target_weight ) {
            for ( 0 .. $i ) {
                ${$refs[ $_ ]} -= $drop;
            }
            $curr_weight = $lowered_weight;
        }
        else {
            use integer;
            my $target_loss = $curr_weight - $target_weight;
            my $div         = $target_loss / ( 1 + $i );
            my $rem         = $target_loss % ( 1 + $i );

            for ( reverse 0 .. $i ) {
                ${$refs[ $_ ]} -= $div + ( $rem-- > 0 ? 1 : 0 );
            }
            last BAG;
        }
    }
}

sub display ($aref, $target) {
    my $r = '';
    for my ( $i, $wt ) ( indexed @$aref ) {
        $r .= sprintf "  %2s: {%s} (%d)\n",
            "#$i", ( '=' x $wt ), $wt;
    }
    $r .= sprintf "Weight %d, target=%d\n",
        sum(@$aref), $target;
    return $r;
}
[download]

Note that, having brought the four highest weights down to 16 but still needing to trim one more character, it took it from the bag that was originally the lightest of the four (#0), thus never violating the original ranking.

$ shrink 79
Before:
  #0: {====================} (20)
  #1: {===} (3)
  #2: {=========================} (25)
  #3: {==========} (10)
  #4: {===} (3)
  #5: {========================} (24)
  #6: {=========================} (25)
Weight 110, target=79

After:
  #0: {===============} (15)
  #1: {===} (3)
  #2: {================} (16)
  #3: {==========} (10)
  #4: {===} (3)
  #5: {================} (16)
  #6: {================} (16)
Weight 79, target=79
[download]

Plugging this into my simple-minded CSV columnizer gave me exactly what I wanted. It remains to be seen if I'll ever want to apply more sophisticated, data-aware methods of narrowing. :-)