A sudden reduction in the Sun’s gravity would trigger huge earthquakes as Earth shifted in its orbit, but it’s hard to think of anything that could cause this. A slower reduction would simply lead Earth’s orbit to slowly spiral outwards and slow down slightly.
In fact, this is actually what’s happening, as the Sun loses a bit of its mass each year, converting it to heat and light. But the effect is very small (about 0.25 per cent of the star’s mass since its formation), and a gradual brightening of the Sun as it grows older means Earth stays warm.
Answered by Giles Sparrow