Heat from other stars. Does the Earth receive heat from the millions of other stars in our galaxy? Does the light bring the heat and perhaps it cools down on the long journey through space to reach the earth and therefore no significant amount of heat arrives here?
While we do receive heat from other stars, the question of whether this heat is quantifiable is debatable.
You can also look at it this way: The Earth would cool to 2.7 Kelvin (270.4°C) if the Sun and stars were magically turned off. Compare that to the pleasantly warm planet we experience thanks to the sun.
Heat from other stars
The stars in our galaxy are extremely close to us in a cosmological sense. Even the Andromeda galaxy is extremely close. The light we see from the stars in our galaxy is roughly equivalent to the light they emit.
At very, very large distances (much, much longer than the distance to Andromeda), the cosmological expansion of space causes the light to be redshifted. The amount of redshifted light gives an indication of the distance to a distant object.
We receive a tiny amount of energy from the cosmic microwave background. This radiation was not emitted by stars. It marks the transition from a very hot and opaque universe to a cooler and more transparent universe. The universe went from opaque to transparent when the temperature dropped below 3000 Kelvin (2726.85°C) or so. Now this light has an effective temperature of only 2725 Kelvin (2451.85°C).
One way that stars can affect our weather is through the influence of cosmic rays on cloud formation. It appears that cosmic rays can trigger high altitude clouds. The effect of those high clouds on the weather is less clear.