In most of these "I don't want to offend them but I want to do this other thing" cases, honesty is the best policy.
Most often, if you offend somebody, it's going to be because you caused them to feel like you participated in the negotiation/transaction in bad faith — leaving them without a fair chance, thus wasting their effort in an exchange they didn't have a chance. No one wants to put effort into something where they don't have a chance, and organizations and people alike actively avoid parties that they fear will take advantage of them.
Example of bad faith
They offer, you accept. Two weeks later, you reneg, saying your old company wants you. They might feel like either you used them for more money (as a safety net in a bluff), or you're flaky, but either way, you didn't give them enough information to truly compete and it possibly indicates low integrity. They had no chance to really get you, and they put a lot of effort in, leaving them with a sour taste.
How to act in good faith
In this case, you're right to be worried, since it seems like you might not be completely sure why you are reconsidering (since you haven't really told us).
Remember, the base assumptions when you seek out (and especially when you accept) a new job are that something about the old job was not good enough. It could be:
- Money
- Title
- People
- Job satisfaction
- Stability
... and many other things. But, I would say that from experience, it's usually not just money. Following that, most companies are willing to be more flexible than you'd think about money.
You've been given new material information, that you didn't have access to when you accepted (Company C purchasing Company A). This is out of your control, and it is reasonable for to reconsider based on factors out of your control.
However, considering that Company B has put effort in to you and may have momentum, your reasoning should be fairly strong. It's a different situation than if you were at a simple fork in the road. You will be changing direction.
So, for Company B to understand your reconsideration, they need to know why it matters — so that they can compete with it if they'd like to try.
If it's only the money, then that might be OK, but you could end up coloring yourself in a certain light. There isn't one universal way this is viewed (for example, it might be much more typical of sales people to make a decision based on money alone than for software engineers) — but it is a risk you take that they don't like it.
If there are more differentiators, the best path forward is to be honest about all of them. After all, in any transaction, the best situation is where the arrangement is completely mutually beneficial. If they are not going to be the best fit for you, then it's better that you let them know now.
If there is something they can do to persuade you, I would know what that is before you talk to them and be prepared to tell them what it is.
How to actually bring it up
Once you know exactly why you don't want to simply go forward with Company B, you need to take the information to them honestly, and see how they react.
This will involve typical negotiation tactics, which I am no expert on, but your situation is essentially that you have two offers and are deciding between them. There is a wealth of information online about how to play one party against another, but in this case, remember that Company B is more analogous to your own employer than your new offer from Company C.
This might be in the form of an email or phone call like this:
Hello, representative from Company B. First of all I want to thank you for your patience while I wrap things up with Company A. I wanted to let you know about some new information from Company A. When we talked, I mentioned my dissatisfaction with Company A because of [REASON X]. Company A has just revealed that they are being purchased by Company C, and I have been offered a position as [blank]. [Talk about why this changes REASON X for wanting to join Company B]. [REASON Y you want to join Company C], is an important factor in my decision because [talk about why]. What can do for me [with respect to REASON Y], as I consider this offer from Company C?
Again, we don't have a lot of information (other than money) about why you are considering reneging your acceptance of the offer from Company B. But, it will be uncomfortable, but it's business, and as long as you maintain integrity, professionalism, and give Company B a fair chance, you should be able to get through this.
