There are a number of solo tents around the 1 kg mark (various Terra Nova Lasers, Vaude Power Lizard, Helsport Ringstind Ultralight, Easton Kilo etc). A sleep system can be had for even a bit less than a kg: Thermarest Neoair or Exped UL Basic mattress, PHD Design Minim bag. If you intend to camp in colder weather, add a couple of hundred grams (for a Thermarest Neoair All season or Exped Synmat Basic mattress and a warmer bag) and you will be covered for that too. A cartridge gas stove comes in under 100 grams, and a pot a pan and a grip will weigh about 200 grams together (Trangia UL 27 parts, available separately). Remember, however, that with stoves the fuel is the heavy item.
This is about the lightest sensible gear. You must realize, however, that even an extra 500 grams will give you rather a lot of extra comfort. Finally, this is fragile and expensive stuff. If you are prepared for slightly heavier stuff, you can save money. Examples would be the Wild Country Zephyros tent, the various Exped Basic mattresses (not even heavier), and an Alpkit Pipedream bag .
Willem