Sure weather will have a effect.
Try using the weather calculator on my website,
direct is Weather cost to performance

Make weather changes with it and see the effect it has. Hot air adds to the correction factor of HP/Tq which is a loss of performance where colder airmass would increase performance so it clearly has effect to AFR and fuel trim values

You see a hugh effect to weather to AIR effect on performance.

Clearly you know in summer heat engine does not perform as well as nice fall or spring weather so air quality effects AFR and reason why using the MAF is much better adjusting tool for the PCM then those people deleting the MAF and use VE speed density as to how PCM determines how much fuel to add to qualty of airmass.

As to tune corrections I slant on the lean side as long as there is no knock pulling timing so there is no rule that LTFTs must be a perfect zero being as long as STFTs are +/- 5% PCM ignores LTFTs and does no correction to them