Angie, it's generally accepted that you can't do both at the same time, with the following exception: Newbies to weight lifting can make impressive loses in fat and equally impressive gains in lean mass, simultaneously.

Why is it that the rest of us can't? It's all in the food you eat. Any fat loss or muscle gaining plan will be 20-30% the exercise and 70-60% the food you eat. You eat very differently for each objective. To gain mass you need to eat more calories than you burn, there needs to be a surplus. To burn fat you need to create a deficit between what you eat and what you burn on a daily basis. The two goals don't jive; unless, of course, you're new to this. THen all bets are off.

The window of opportunity lasts a few months, possibly a year, FYI.

If your goal is fat loss, then I'd suggest you pick up the weights - cardio is great for creating a caloric deficit and for working your heart, but it is nothing when compared to weight lifting when you're talking about burning fat. Resistance exercise helps build active lean tissue, which will burn fat for you even when you're sitting watching TV (or sitting on the computer ). While you may notice the scale doesn't dip down as quickly as it did before you began lifting, you will notice that you're dropping sizes a lot faster.

HTH
Nat