"Over clothing" is dangerous, because they will almost never put on helmet, gauntlets or boots. That green checkmark in the equipment menu just means that the item is available to and claimed by them, it doesn't mean they are actually wearing it. Check DT or inspect unit.
If available civilians will all wear 1each of: robe/dress/coat, tunic/shirt/vest, cloak, cap, hood, trousers, socks, shoes, gloves, mittens.
This is also how embark and migrants arrive.
So the cap keeps them from wearing a helmet, gloves and mittens the gauntlets, socks and shoes the boots.
While it's possible to get them to wear socks and mittens with boots and gauntlets it tends to be very problematic and is best avoided.
Also clothing weight adds up. I see a lot of people say not to armor up unskilled dwarves and I disagree. Armor and shield will save your elite marksdwarves asses when they do stupid shit (and when don't they)
Helm, mail shirt, breastplate, greaves, gauntlets, high boots - preferably steel/candy. Shield. Shields for everyone! Do not bother with bucklers. Do not bother with leggings. Do not bother with leather armor, it's just about worthless. If that's the best you can do better to just give them a weapon and shield with over clothing orders.
If you want to get fancy and add hoods, cloaks, robes, trousers - That's when you should consider their armor skill or lack thereof since they add weight for little gain. Avoid socks and mittens. You'll wind up with dwarves wearing only 1 boot or gauntlet and that is the foot/hand they will get hit in I guarantee it!