Having duplicate entries in a tag does not impact the chance of that entry getting randomly picked.

In the attached datapack. There is an enchantment tag with 4 entries for protection and 1 for mending. Using this tag with the enchant_randomly modifier. The chance of getting mending is expected to be lower than 50%. This is not the case.

{
  "function": "minecraft:enchant_randomly",
  "options": "#weighted_enchantments:weighted_list"
}

 
When using the same modifier but using multiple options, the chance of getting mending is much lower.

{
  "function": "minecraft:enchant_randomly",
  "options": [
    "minecraft:protection",
    "minecraft:protection",
    "minecraft:protection",
    "minecraft:protection",
    "minecraft:mending"
  ]
}

How to recreate

1. Install the datapack
2. Run /loot give @s loot weighted_enchantments:using_options
   → Observe the rarity of getting mending
3. Run /loot give @s loot weighted_enchantments:using_tag
   → Observe that the chance of getting mending is much higher