I rode my first double on a ~'85 7-speed. Yeah, if hills are really hard, you should go to an 11-34 in back if the bike doesn't already have a cassette that size. Which might mean a new rear derailleur and a new chain. As you get stronger, you can go back to a smaller cassette. Being able to sit and pedal uphill without a lot of drama is key. Oddly enough, cycling is all about riding uphill. Bizarre, but that's how it is. Talk to your bike shop, see what's available. The weight of your current bike is not an issue.