Beth, whatever you decide to do you will find a body of running opinion that will back you up. Some are keen on weights and others wouldn't dream of risking their precious legs in a gym. And many recreational runners just never get round even to thinking about doing weight training, and Peak Performance says we do all the wrong stuff anyway.
I enjoy doing weights. I like having visible muscles in my arms and calves, and abs the my son bounces off when he headbutts me (it doesn't half hurt when his shorter sister copies him, though!), and like Mij I do lots of light reps rather than the stuff where you need a spotter to lift the barbell up and put it down for you. My programme is simple - I do one or two Bodypump classes a week, and sometimes a few press-ups and crunches and calf raises between times. The exercises are of the low-weight, high-rep endurance type, which is what we runners need. And I am not one bit bulky!
Remember that even though you don't run on your arms, muscle is metabolically greedy stuff and eats its way through 30-50 calories per pound per day just ticking over. So the more, the better, if you like a full plate but don't want to gain weight.
Give it a whirl. You can always stop if you don't enjoy it.
Cheers, V-rap.