I play live poker and I normally buy in 200 big blind in a £1 - £2 game, which is £400. I consider this as a reasonable buy in. However, because there is no upper limit in the casino I play, there are some player who buy in £2000 which is ridiculously deep. I understand that their effective stack is the same as me, but it still put mental pressure on me that I could potentially lose a super big pot to them when I increase my own stack.

Any advice how do I overcome the fear of losing a super big pit in this situation? I feel I’m out of my comfort zone when the pot is over 2k.

Whenever a deep player sits to my left, I start off playing slightly tighter and folding marginal holdings that I'd normally call or open. I do this to get a feel of my opponent.
After understanding what type of player he is, I'll either go back to my original strat or tighten even further up if he's a maniac etc.

Stack sizes are intimidating at first but the
feeling of intimidation usually goes away after a few orbits. If you're still uncomfortable after 30 minutes, you should get up from the table and move down in stakes.

Unfortunately no book or advice on here will ease your mind and anxiety about this situation. The only way to beat this is with experience. The more you force yourself in awkward situations, the better player you become. Gl and best of luck at the tables.

You should ask for a seat change

What BCloud wrote sounds about right. I actually prefer good, deep players to my left now, but that's after lots of hours playing in a deep game. I prefer the weak players to my right so I can take advantage of them.

Trust me, you will get used to playing in big pots. Until then, tighten up and pay attention -- and don't let them bully you.

If you are uncomfortable, leave or ask for a table change. And if you are up so much that it would tilt you to lose, definitely go home!

You seem to equate a big stack with a superior player. Like everything else in poker, this depends on other factors, such as how did they get that stack? When they buyin for huge amounts, what are the other stacks at the table? Ultimately, however, it depends on how they play.

I know of two main reasons people overbuy in a game: to entice people to come and get it, if they can. Or to make sure they have lots of money to gamble with.

Yeah if u get afraid of being deep and losing a big pot, you need more money to begin with