Will this regime help me lose weight and "tone up" a bit? And how long before I'll notice a difference?

The only real way to build muscle m is to actually consume more calories than you can burn, so that your body can use the excess to build muscle. However, since you only have 2.5kg weights, I'd suggest just sticking to your cardio/calisthenics routine you have going, eating whatever feels comfortable, and saving up money until you can afford a gym membership and some eggs.