It did not occur to you that being appropriately camouflaged would be advantageous?
The RAW source for "sneaking clothes" or anything else that gives positive circumstances to a d20 roll is (PHB p.7):
Advantage reflects the positive circumstances surrounding a d20 roll, while disadvantage reflects the opposite.
In the right circumstances (i.e. darkness) being a black cloak would help you hide (by the way, due to the way the rods in the human eye work, dark green clothing is much more effective than black - but then, not everyone in the world is human, are they?). This is in no way comparable with a magic item or spell (pass without trace) which grants its effects irrespective of the circumstances. To get similar benefits the PC would need desert camouflage, and jungle camouflage, and winter camouflage, and etc. etc. which would become both cost and space prohibitive.
The advantages of advantage [sorry] rather than a strict bonus are:
- it can be taken away by disadvantage
- it doesn't stack with other sources of advantage
- it doesn't make the impossible possible (a 20 is still the best you can get)
- it is not "worth like a +2 or +3 on average"; its effects are much more subtle and depend entirely on the target DC - see http://anydice.com/program/ba
This might lead other players to try to do the same thing…
And this is a problem because…? Player's trying to give their characters advantage is great - it means they are thinking about the best way they can overcome the challenges you give instead of "[monotone] I rolled a 12; did I do it?"
Remember: A Dexterity (Stealth) is opposed by a [passive] Wisdom (Perception): each of those has (dis)advantage independently. The cloak gives advantage to the Dexterity (Stealth), bright light might give advantage to the [passive] Wisdom (Perception). It might seem that this is the same as giving disadvantage to the Dexterity (Stealth) but it isn't because:
- Allowing the player to roll 2d20 instead of 1d20 makes them feel good about their cleverness in thinking of the cloak
- They are mechanically different! See http://anydice.com/program/87f0 which compares a Dexterity (Stealth) with +5 against a Wisdom (Perception) of +0. Indeed, they even change depending on if there are opposed active rolls or one is a passive value. Note that these are the exact same circumstances but the chance of success varies from 48.33% to 88.75% depending on where you choose to apply the effects of bright light (advantage to the seeker or disadvantage to the hider) and if the seeker is actively looking.