You will eventually hit a point that raising your bet may cause more heat than the gain in EV is worth.
Already a lot of decent answers here (for a change), but I'll ad my thoughts too.
When your BR increases, I would say it's ok to increase your stakes, as long as your RoR can stay constant, or even better, be lowered. I always chose to increase my stakes when my BR took a nice up-swing, but I always try to maintain the same low RoR or operate on an even lower RoR. But the answer to this question is completely subjective and many factors must be considered:
1) How much risk are you willing to take on?
2) Is your Bank replenishable?
3) How comfortable are you with bigger losses?
4) Will higher stakes cross your local casino's comfort threshold?
5) Can you raise your stakes while keeping your RoR to a comfortable level?
Something that I've learned over the last few years; many new AP's constantly come on the boards (I also used to be one of them) seeking answers that are very cut and dry. Black and white. Unfortunately, once you get passed the fundamentals and the technical side of this game, many of the answers you seek won't be so cut and dry. Many variables constantly come into play, so the best thing you can do is take all of the information that you have and try to make the best decision that fits your situation best. Everyone's approach is different, so you need to explore all your options and try to decide which one works best for you and your particular situation.
Good luck
Something else that I don't think that has been touched upon is this -- do you need to up your max bet? Not sure if OP is professional or going toward that road, but you don't necessarily have to increase your max bet. Ya know, if you're playing recreationally and CC BJ is not your main source of income, you could take money out of your BR and spend it on something you want or need (assuming it doesn't have a significant increase in ROR, yada yada yaa). What's the point of making money if you're not gonna spend it?
Not saying you should spend any and all winnings or anything like that. But depending on your circumstances, there are other ways to invest your money, doesn't have to go right back into your BJ BR.
Granted, if you're in the process of growing your bankroll and all that stuff, if I were you, I'd be re-sizing my max bet when applicable. It wouldn't even be a question.
"Everyone wants to be rich, but nobody wants to work for it." -Ryan Howard [The Office]
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