- Temperatures (and resulting weather) would largely be influenced by the exposure to sunlight and the tidal forces due to the planets gravity and the moons rotations.
- The height and volume of the tidal waves may significantly influence atmospheric pressure(thus wind) only if they're very large (single or double digit percentages) compared to the moons size and its atmospheric thickness.
The tidal waves as well as the day-night cycle are determined or additionally influenced by these rotations:
- The giant planet rotates around the sun.
- The moon rotates around this planet.
- At the same time the moon has its own rotation.
All these rotations will determine the day night cycle (and weather) on the moon (light from the sun reaching a surface portion oriented towards the sun).
Depending on the speed the moon rotates around the planet and the moons own rotation these will shift along the planetary year (one full rotation of the planet around the sun).
Depending on the speed the planet rotates around the sun, the day night cycle on the moon will shift and stretch / contract during the planetary year.
The day-night cycle will vary and may inlcude multiple partial(longer / darker nights) days & nights depending on the moons rotation around its axis and its rotation around the planet.
Similarly the intensity, height and volume of tidal waves will vary as well according to the moons rotation around its axis and around the planet as well as its distance to the sun (may be negligible depending on distance).
Plotted on graphs or 3D models, both, the tides and the day-night cycle will form
local and global extrema (maxima and minima).
This will further complicate your question about the weather impact with smaller and larger cycles.
As has been said, you need scientific advice beyond the scope of this forum if you're looking for calculated, precise enough predictions.
In conclusion I also should point out that this moon might have extreme tectonic movements resulting in very strong quakes and heavy vulcanic activity.
Sounds like a very inhospitable environment.
Evolution of intelligent life faces many difficulties, constantly on the brink of extinction.
Same goes for any civilization building settlements on or below the moons surface.