What should I do with KK in this spot?

The first thing I think is not so good is your 6bb open pre. Why this big? From BTN you can steal quite wide and do it with a smaller sizing, so when you hold a good hand your sizing should be small then too. Only exception is if villains on SB and BB are recreational players and you know they will call such a big open.

I think the bet sizings are slightly too big. When you face a turn raise I think it is best to fold.

You have to remember that when you make this big bets, villain will call with narrower range.

I was having a great session, another thought that came into my head before I folded was, do I want to call this and turn it from a winning session to a losing session...

This is understandable thinking but something you want to get rid of. Poker is a long term game and you shouldn't focus on quitting your session on profit. If you face this kind of situation and believe calling would be +EV, then you must make the call even though you might sometimes lose and your session might end up being negative.

Wow. A lot of misconceptions here.

Preflop:
Your raise is BIG. Its not wrong to go big if you have a good reason (like that they will call a lot regardless of sizing). But the fact its a big raise will come into play later

Flop:
Betting big is correct here because you will get a lot of calls and your hand is ahead of his flop calling range. But the reason you should bet big is to get value. Not make our oponent fold his hand. Because if he starts folding everything that you beat, what will he continue with? Hands that beat you.
And an A or a flush card falling on the turn.. although it is going to be bad for your hand, the reason you dont want those cards should be that worse hands will have a hard time continuing against you and thus if you bet you will isolate yourself mostly against better hands. Thats why you bet big on the flop - to get as much value while you still can.

SB's range:
The 3♦: is one of the safest cards in the deck for you. It completes only 33 that he would probably fold on the flop and A2.
A normal player's calling range against a preflop raise is going to be the tightest because he is out of position. Even though you raise big preflop, you both are deep so he may call with pocket pairs and maybe suited connectors. But he shouldnt call with 2♥:3♥: or 9♥:6♥: for example. So his range should be reasonable, not wide.

Turn:
Its ok to go big again and be prepaired to fold vs raise. But overbet is a little bit of a stretch. The bigger you go, the more hands you beat are going to fold. Betting like 30 is much better.
Check-call flop and check-raise turn is one of the strongest lines villains have at these stakes and its so rarely a bluff that you shouldnt really consider it. So folding is correct. But not because you had a winning session! Folding is correct because it saves you money against villains nut range.

There isnt a river, so I guess you share your plan for the river?
Why would you want him to fold the river? Making him fold a set on the river is impossible. Making him fold 2 pair is such a long stretch. So basically if you go all in, all hands that fold you beat anyway with your big pair. And depending on what opponent it is, he may call you with worse but mostly when you get called you will lose. So a big river bet its not only pointless - its bad

Not much to add there.

You bet big, and then you hope and pray he calls with a worse hand. That's how you make money at poker. Your present mindset is totally wrong, but not uncommon. Betting to "make someone fold" is the subject of bluffing. You don't do that on the flop with an overpair. You make it holding nothing at present, but with a draw to back things up.

What's with the pot size bet on the flop against one guy (the board is not that so scary either)

A little tip : leave the table if you have 200+BB. You seem not too experience in cashgames (no offense) so I recomment not to play deeper than 200+BB.

This is great feedback.

First to Turok yes I am still new to this. I thought that I should leave the table to go back to 100bb and in the future if I get to 200bb I will do this.

It's amazing because as I was typing my hand I realized what I had done. I keep a notebook and wrote down my thoughts after my hand and it's good to see that the mistakes I think I made were correct that they were mistakes.

The most eye opening thing about these responses though is about my mindset on getting him to fold which I didn't realize was the wrong mindset until now. I think I have fallen into this trap because I'm afraid to lose to a better hand on later streets and I am just trying to get paid now.

I think I formed this mindset from when I don't hit the flop, but I open raised so I C-bet on the flop on a dry board to get my opponents to fold.. but I see here maybe I have the wrong mindset because at the time I did clearly have the best hand on the flop and should have lowered my bet sizing, not bet like a crazy man..

After I typed out my post I went on PokerSnowie to analyze this hand and pokersnowie also suggested half pot bets, but also suggested calling his All In on the Turn.

When you are cbetting you should basically think your range, villains range and the board.
That might be difficult but it will come to you when you gain some more experience.

For example when your perceived range is weak and villains perceived range is strong, it is correct to choose a larger sizing with all of your hands. So, the hand you are holding shouldn't be the only factor when choosing a sizing.
If you have correct amount of bluffs and value hands in your betting range, it doesn't matter if you are betting as a bluff or as value.

Better fold...SB flatted with pocket pair and made set.

Put it this way: what can villain have he raises with (bluff or value) and what can you beat.
Imo, there are many more hands that crush you (A2, 45, 67, 33, 44, 55) that what you beat (78, 99, TT).