You might want to edit your post to clarify that weight does not affect the probability of a given selection.

Two ideas

You could pre-calculate (perhaps write to data files if there are many) all possible items and their strength/weight values. If your list of possible weight values is dense (few skipped values) put an array of items at each weight at a coresponding index in a master array. So:

my @items = (
    # 0
    [  'sword', 'mace', 'turtle' ],
    # 1
    [ '+1 sword', '+1 mace', '+1 turtle' ],
    # 2
    [ 'frost sword', 'frost mace', 'frost turtle',
      'flame sword', 'flame mace', 'flame turtle' ],

    ...
);
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If the set of weights is sparse, you might use a hash instead.

Then if you want to select a random item of weight 3-5, you can do:

my @in_range = map @{$items[$_]}, 3..5;
my $item = $in_range[ int rand( @in_range ) ];
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Another way, would be:

1. Pick a random weight value in your range. eg 7
2. Prefix list is sorted by weight, and starts with an entry for ['' => 0].
3. Find last prefix with weight less than or equal to weight. Eg. Pointy (6)
4. Pick Random Prefix up to max prefix from last step. eg. Acid (4)
5. Set plus value equal to desired weight - prefix weight. Eg. Plus = 7 - 4 = 3
6. Result: Acid +3 Sword