Are we assuming 100bbs in a 200NL game? Absolutely. Every time. If you even have to second-guess getting all the money in preflop with literally the best starting hand in NLHE then you are fundamentally missing what the game is all about.
odds and probability, having an edge, and maximizing value by making +EV plays. All in
equity preflop does not get any better than that. Now, having said all that, if $200 is ALL I HAVE, then I am playing at the wrong limit. You should not take your whole bankroll to the table. With that amount of money 10NL is the absolute highest you should be playing, and only if you're a winning player who knows when to dial down the stakes when the downswings occur. If I'm properly bankrolled for 200NL (which would be a substantial amount, depending on your winrate, risk adversity, and lifestyle), then being stacked by getting it in the best possible situation before the flop, in a
cash game (my tournament life isn't at stake here) means I lose a buy-in. NBD. Yeah, you will lose a fair amount of times in that scenario, but statistically-speaking it is the most profitable PREFLOP situation to be in.
I say all this as you said "if I had AA preflop" but you also have JJJ... of diamonds in your question. Does that mean we are now POSTFLOP and the board flopped 3 jacks? Then the play here is substantially different, and we need A LOT more information about how you ended up in a situation where your buy-in is at risk on that board. Truthfully I'd be more terrified of that in PLO/PLO8 than in NLHE, but still without knowing anything about the action so far, I can't say for certain whether or not I lay down American Airlines in this spot.