Directs of different levels

 I am not sure I understood the structure.  Is this level issue related to salary rate, function, professional qualification, years of experience?  If they are your directs (you run one-on-one with each one) they should all participate in the meeting regardless of the level they are in.  

I could make an analogy let´s say having people from different professional backgrounds working for you.  Let´s say you have engineers and chemists working for you for example, you would not run a separate meeting for each group concerned that the chemicts would go aroudn talking to other chemists within the company or something like that bout what was discussed on the meeting.  If you hold the meeting on a professional manner and make sure everyone does the same (give adjusting feedback if they don´t), there is nothing to be worried about.  People just have different roles and responsibilities and they are all worth the same (for you as their boss) regardless the level they are i, and if they have to work in cooperation you need to run the weekly staff meeting with all of them.

One of the purpose of the weekly staff meeting is to enhance communication between your team, and if they are from different levels and there is un unhidden hierarchical structure that level 1 directs are somehow above level 2 directs even if it does not show on the process or organisational charts, much more so you must have all of them in the staff meeting.  Unless there is something wrong with the organisational chart, and really only level 1 directs should be reporting to you, and level 2 directs to the level 1 and so forth.  But if per the process each one is responsible for it makes sence to have them report to you, then they should be all in the meeting.

I don´t know your company structure, but it sounds like maybe you are complicating it when there is no need to.  As the saying goes: "Why do it simple if we can make it complicated."

We do need to be concern about people´s feelings (quite a bit in fact and probably more than the average manager does), but really it is not about how people feel, it is about what is effective for the job that needs to be accomplished (manager-tools).  They should just get over the awkward feeling if in fact it is there, because it should not be.   I believe I might be guessing too much here based on the little information on your comment, but perhaps you are an S type manager and overly concerned about how people feel.  if you are, my suggestion is for you to listen to the S-manager podcast, it might help you.

Sounds like you are now Team B's manager.

Hence, I see no reason why you should not be doing O3's with them as well. They are your direct reports now.

 Ok, I understand it now, it sounds like you are in fact accumulating two roles.  If the teams were bigger I would say have a meeting with level 2´s (as a level 3 manager) and another one with level 1 (as the level 2, Team B leader, which role you are accumulating).

But as you have only three people there, one team A leader and two team B members I would have the meeting with the three of them to facilitate things (of course one-on-ones with each of them individually).

The other thing which you also may consider, say if Team A is also small, two team members, is to have the staff meeting with all five, plus you, six.  The only thing you have to be careful there is not to bypass your team A leader, you still want him or her to have the one-on-ones with his/her team members.  The staff meeting would only be for people to report and share information which is relevant to all.  If you decide to do that, talk ahead with your team A leader and explain the objectives of the meeting and make sure she still assumes the responsibility for the work of her team.  I find that up to 8 people in a meeting is about the limit, more than that it becomes a wast of time.

Choose one way of handling the meetings, do it for a while, give time to see how the dynamic works, and how effective the meetings and accomplishments of the week are, observe and if need to change you can always change it.  There is no really right or wrongs.  There is only what is more effective.