Equator and Hours of Daylight
The Earth's equator is about 0.006% closer to the sun than the Earth's mean spin axis, so the effect of proximity to the sun on daylight hours is so small that my calculator - which has a register of 10 significant figures - can't even discern any difference. A rough back of an envelope hand calculation indicates less than a millionth of a second difference in daylight hours between equator and the Earth's mean spin axis. So the effect on the weather would be indeterminate, and vastly less than caused by orbital variations, solar storms, fluctuations in solar luminosity, seasonal cloud variation, etc.