Well, NEF still sells a .30-30, with open sights. It is not real light, has a fairly heavy barrel. BUT, H&R used to make a .30-30 in the model 58, and others, and they had tapered barrels. Mine has the 22 inch barrel. They came with hardwood stocks, which I replaced with current production synthic stocks, as they weigh less. Mine came with open sights,which I removed in favor of a scope. For a really light outfit, I'd look for one of these, probably available IF you can find one for about $125-150. They are drilled and tapped for the current H&R/NEF scope mount, which means you can add peep sights sold for the current one ( unknown if you might have to change front sight hight).
On one of mine, I put a very nice reciever sight, finger adjustable for W&E. Two points to keep in mind if you consider this route: 1) These frames are case-hardened, and are not as strong current H&R/ NEF rifle frames, so if you handload, don't get carried away. 2) Two versions exist, one with screw-on forearm, like current issue, which will allow you to add current stocks of any kind ( although barrel channel may be "generous") the other version ( earlier?) has a snap-on forearm, which later forearms will not fit on.
One other point, in an old issue of "Gun Digest" I once read where it was somewhat common to rechamber the older .30-30 H&R to .30-40 Krag, for an increase in power ( using factory ammo). Apparently the H&R would hold up fine to that conversion, alshough with current ammo I guestion how useful the conversion might be.
One other thing, NEF sells an "ultralight" in .243 that might be what you like, if you care for the smaller caliber.
Lots of info on the H&R/NEF forum up towards the top.
Mark.