Fallout – How much carry weight does “Pocketed” add

Carry weight does not have any effects on stealth.

Your ability to sneak is affected by 8 different factors:

• Equipment weight: Although you said there was no difference, there is a difference if you walk. The heavier the armor or weapon, the further you'll be heard if you move. However, if you stand still, your armor weight won't affect you at all.
• Light sources: Light sources also influence your ability to sneak heavily. However, this only affects you if an enemy has a clear LoS on you. If you are in a lit room with no enemy being able to see inside, the light does not affect you at all.
• Your agility skill: The more agility you have, the more difficult you become to spot when sneaking. This affects you in both moving and not moving.
• Perception of the enemy: This is also a huge factor which both affects you moving or not moving.
• Distance: Obviously, the further the enemy is away, the hard it will be for him to spot you.
• Any form of contact: If you touch an enemy, he will immediately spot you.
• Loud Weapons: Any form of attacking an enemy will make them spot you. However, silenced pistols, melee weapons and grenades/mines will not break your stealth, although it will cause the caution alert if you do not kill them in one hit. Grenades always cause caution alert if there are any alive enemies in the area.
• Special gear: There are several modifications like shadowed which can improve your ability to sneak. Also, gear obtained from legendary enemies can have a stealth-improving effect on you.

Your pip-boy (includes the torchlight) do not affect stealth at all as you already found out. You can also listen to radio while sneaking and nobody will notice.