https://www.cardschat.com/replayer/39A5ybZMP

Been wondering about how I should be playing from the BB WRT 3betting. Do I want to be playing a more linear strategy in general? Playing on party so don't ever have lots of data on villain tendencies.

In terms of the hand posted. Would probably prefer to just call this hand.
As played I am a bit unsure about whether or not to cbet.
I have a hand that is extremely vulnerable but I am OOP and the texture is not one that I want to be cbetting here all the time.
So my questions are should I cbet this particular hand and for what sizing?
My gut feeling would be to cbet for about a half pot sizing as villain can call with a lot of hands that have high equity that I beat and can also fold out some other Ax and broadway combos with no BDs.