Because of the great elevation gain on a Kilimanjaro trek, you will experience all kinds of weather. At the beginning of the climb, in the rainforest, expect it to be hot and humid. Most likely you will be comfortable wearing just a tee shirt and shorts or trekking pants while walking.
However, it gets cold pretty fast. Even on the first night of your climb, it will be chilly. A fleece jacket and knit hat will be required to keep you warm.
As you make your way between visit this campsites, most commonly you will be fine with just one or two layers on top, such as a baselayer and a thin soft shell jacket, and one layer on bottom. As long as you are moving, or in the sun, it is not cold. However, if you stop for an extended period of time, or the clouds come, it is cold. It is a good idea to either put on a jacket when you stop for a break, or to not stop for any longer than 5-10 minutes at a time.
On every successively higher campsite, it will be colder. Most people like to hang out in camp wearing a down jacket and fleece pants. It frequently drops below freezing at night. You may wake up to ice crystals on the inside of your tent.
Some people make the mistake of trying to cover up the tent’s built in ventilation in order to keep cold air from entering the tent. But what this does is cause a build up of moisture in the tent. This actually makes you colder! The vents are there for a reason – do not mess with it!
On the summit night, it can be very, very cold. You guide will advise you what to wear. Most people seem to do well with four layers on top – baselayer, soft shell, insulated jacket, hard shell, and three layers on bottom – tights, fleece pants, rain pants.
Once the sun comes up, it warms up fast. It can be below zero overnight, then as much as 30-40F in the morning sun. So remember to strip down and rid yourself of maybe 2 layers on top and a layer on the bottom for the descent.