Does the Sun's cycle influence our weather?

The Sun's magnetic field constantly changes - the Sun's polarity reverses every 11 years. This activity changes the number of sunspots on the Sun's surface - this then peaks at the 'solar maximum'. The Sun's activity cools areas on the Sun meaning they appear darker. The solar cycle can also cause small changes in the Sun's heat and light output. Some studies have shown some link between few sunspots and cold winters in Europe. Although it's unclear the Sun's cycle could influence our weather.

If the Sun's gravity was reduced what would happen to us?

A sudden reduction in the Sun's gravity would trigger massive earthquakes on earth as we were shifted along with Earth's altered orbit. However finding something that would cause this would be very difficult! A slow reduction in gravity would mean that the earths orbit would slowly be altered. In fact what happens is the Sun's mass decreases very slightly converting it into heat and light. To put this into context the mass that the sun looses each year is about 0.25% of the sun's mass since it first was formed. Also as the Sun grows older the Sun also gets brighter which means the Earth stays warm.

What causes heat haze?

The appearance of any object depends on the optical properties if the air between you and the object or person. These are determined by the density and temperature of the air, so any source of heat, maybe from a barbecue or the sun can cause uneven changes to the density of the air. These changes produce optical distortions which we know to be heat haze.