1kg hand weights are very light, however, it really depends on what exercises you are doing with the weight in order to maximise your results! If you have been doing no exercise before you start using them, then any extra calories burned will help towards weight loss. You will need to watch your nutrition at the same time though!
If you don't want to invest in any heavier weights then perhaps you could look at doing exercises which maximize the calories burned with your 1kg hand weights. I would recommend boxing with them rather than using them for just strength training exercises.
I personally use 21-1.5kg hand weights when I do all my cardio workout dvds in order to add extra intensity and burn more calories. They say that your arms add 12% of your overall intensity/calories burned.
If you are unsure of how to use your weights to do boxing movements, perhaps you want to look into purchasing a workout DVD that will teach you some basic moves. Billy Blanks Tae Bo is one of the veterans of kickboxing boot camp DVDs and he has a huge selection to choose from – some shorter so you don't have to increase the amount of time you are exercising if you don't want to. I also have a whole lot of my own workouts, which use light hand weights listed in the Barlates Body Blitz Upper Body category of my store.
Other than that you might want to consider purchasing a resistance band, as these are excellent for strengthening your muscles without costing a lost. Resistance bands also let you work at your own pace in that you can gauge how much resistance you want to use in each given exercise by tightening up on or loosening the band.
