The problem is you've got conflicting requirements, plus a limited budget so silly priced ultra lightweight stuff is out of the question. You need comfort, which means having wider tyres with plenty or air volume. Wide tyres are heavier than skinny ones, leaving rolling resistance aside. If you need wide tyres, you also need rims wide enough to mount them, which again are heavier than narrow ones. Unless you are prepared to compromise on comfort, the wheel and tyre weight is not avoidable. That leaves the frame, gears, and anything else fitted.
Ditching the gear mechanisms & multiple chainrings would be the obvious next choice, but since you have hills, single speed isn't an option. Running a fairly small single front ring and getting rid of a triple plus the front mech and changer etc would save a little, but I would only do that on a short-distance pub bike not anything I was going to clock up real mileage on.
There's nothing you can do about the frame, other than replace with a lighter one. Anything else can only really be lightened if you are starting out with steel bits and can replace them with alloy ones.
In conclusion? Personally I'd just keep what I already had, so long as no suspension fork was fitted, and try to minimise rolling resistance with good tyres rather than go on a weight reduction mission, which is realistically not going to achieve much unless you are willing to spend large. I don't actually consider 30 lb to be especially heavy for a bike anyway, and all my adult sized bikes, with the exception of my newly-acquired 531 Dawes, weigh 30 lbs or over. My 3 speed roadster is around 37 lbs and even at that weight I don't consider it a problem to propel around.