For some observing programs, it may be possible to adjust the observing strategy to take account of the weather during the observing run. But, to quote Barry Clark from the early days of operating the VLA under New Mexico's usually-sunny skies: ``you can't tell the phase stability by looking out of the window''. You must observe to find out how stable the phases are. It is difficult to guess phase stability in advance (except to say that it is likely to be bad because a storm front is passing, for example). But it is also difficult to predict it at the time of observing just by ``looking out of the window". Clear blue skies offer a much better chance of stable phases than lowering clouds, thunderstorms or snow. But they do not guarantee freedom from upper-air turbulence and winds that may also produce unstable phases!
If your program has frequency agility and you are actually at
the telescope, it is a good idea to monitor the phase of a strong
calibrator for a few minutes on a long baseline as you start
observing. Fluctuations of order a radian on a time scale of minutes
are unmitigated bad news. The only possible strategy is to move the
observations to lower frequencies if this makes astronomical sense.
The converse is not true, however. Short-term (minute-by-minute)
phase stability to within a few degrees does not guarantee that the
observations will be of good quality for synthesis. Synthesis imaging
requires stability over the time scale of your calibration cycle
(unless you are going to self-calibrate). You should therefore pay
attention to the phase changes between adjacent scans of your
calibrator, as well as to that within the scans, to assess whether you
have the stability needed for synthesis. If the longer-term stability
is marginal, i.e., of order 
to 
between
calibrations, you might consider using a faster calibration cycle.
The weather is the one area of synthesis observing where you truly do need a little luck, especially if you cannot self-calibrate your data!