Conditioning perk on Heavy Armor tree doesn't support you on sneaking. That perk just takes away the weight from the armor you wear so you have more room to carry items and move a little faster.

What does the conditioning perk do?

The conditioning perk makes to where you aren't even wearing armor when you sneak. That means that it's even better then wearing light armor when the perk is activated.

What affects sneak Skyrim?

Your ability to sneak successfully is determined by a number of factors: Movement: You are hardest to detect while motionless, and easier to spot while moving. Line of Sight: Enemies are much less likely to detect you if they can't see you. Light Level: The darker it is, the harder it is for enemies to see you.