www.exrx.net is a good resource to poke around for all kinds of exercises. They have lists broken down by body part, then ways to strength train that body part with weights, machines, bodyweight, etc. It's not a program or anything - more a directory of the stuff you could put together to make a program - but it's very useful all the same and there's a ton more info, calculators and so on. I'm sure others will chime in with their suggestions too.
And just as an aside - it's not true that the only way to work out with weights is just to go heavy. In some circles it's the 'thing' to claim that only heavy intense low-rep workouts are any good. In reality, most people who aren't trying to be pro powerlifters or bodybuilders will see results from using slightly higher reps and somewhat lighter weights, etc (so long as it's still actually a challenge at the end of the rep range!)
There's a balance between strength and endurance.
I went through an awful lot of ridiculously high rep exercises while training in various martial arts. Speaking from experience, bench pressing your body weight for five reps will increase your upper body strength much more than doing 300 pushups . . . and it's more efficient because it can be done in a short period of time. Extremely high reps with lighter weight tended to limit my strength, but is great for endurance.
There is benefit to occasionally changing the rep ranges in your workout. If you work your way up to reps of five and stall, changing things up to do reps between ten and twenty (with an adjusted weight) for several weeks can really help you. Personally I've had good success in increasing my overall strength using rep ranges from 3 - 20. Regularly trying to hit my one rep max at a lift leads to increased likelihood of injury (for me anyway), and there's little to no strength benefit doing more than twenty reps of anything.
