Like Tyler commented, you don't generally plan to plan something. (Well, unless you're my brother-in-law, who is notoriously indecisive.) Thus, the usual interpretation for
We will arrange a meeting this weekend.
is that the meeting will take place this weekend.
You can technically put a "for" in there:
We will arrange for a meeting this weekend.
but it doesn't change the fact that the meeting will take place this weekend. It does, however, change the meaning ever so slightly. I'm having a hard time verbalizing the difference, but I think it has to do with who is expected to be present: in the first version (without "for"), both the speaker and the auditor are assumed to be participants in the meeting. In the second version (with "for"), there's an implied possibility that the speaker and the auditor are third parties, i.e. they will not be participating in the meeting itself. You arrange for your boss to meet a client, but you arrange to meet the school principal yourself.
If you want to say that the planning is what will take place this weekend, you'll have to expand a bit and rearrange the clauses:
This weekend, we will be making the arrangements for the meeting.
The arrangements for the meeting will be ironed out this weekend.
(But note that you can't put the second example into the active voice: "We will iron out the arrangements for the meeting this weekend" once again implies that the meeting will take place on the coming Saturday/Sunday.)