A major weakness in my game at the moment is exactly as the title states: playing pots OOP as the preflop raiser. How does one go about designing checking and betting ranges OOP of the flop, particularly on volatile flops such as Th9h5s or 2h4c4s?

You need to design a range where you have a lot of ch/calls, a lot of ch/folds and have som c/r. You don't say anything about what position you get called in.

To be cbetting Th9h5s:
I would start ch/c hands like weak Tx and starting to check hands as QT and weaker tp.
Im going to ch/c all my 9x hands and also ch/c lots of 5x, hands like A5.
I will be checking strong hands deep like AA, JJ, QQ with some frequency, esp with a heart in my hand and betting the others.


I will bet KT, QJ, KQ, 87.

I will have lot of gives up on this flop!

I will be c/r hands like 55, 99 and QJhh, KJhh, J8hh.

But its impossible to say exactly what to do when you don't need provide more information.

I

for example we are deep 200bb+,and opp is extremle lose,like to float or raise my cbet

if he calls too much, you just dont bet enough or he thinks your range is too weak. tighten up preflop and enjoy your money, or bet bigger