3 times a week is enough to lose weight, more days is probably better for keeping you in the habit, but if you can only do 3 days, then don't worry.
The way we all lose weight is some variation of 'eat less and exercise more'. For some of us, that means HIIT five days a week or running every day, for others, it is three days of cardio and weights, and for others, it is a walk around the park once a week.
If you like the routine you have then it sounds great. I think the most important exercise is one you like enough to stick with for years. I use an elliptical, light weights, and a dance class for my exercise because that's what I love and I can stick with it. Lots of people love to run, but I don't do it because I would never stick with it - I don't love it.
I would recommend you hire a trainer as soon as you can afford it though (even one session would help), to at least to make sure you are using the weights properly - you don't want to injure yourself with poor form or posture and have your new routine derailed!
BP