The trigger on my hunting rifle has a rather heavy pull and doesn't break very well, will getting a trigger with a lighter pull weight help me be more accurate?
My competition triggers were normally about 2 ounces. However, you can train yourself to use any weight within reason and 7-8 pounds is reasonable for a hunting rifle (people still manage to have accidental discharges). The key is a smooth squeeze directly to the rear, regardless of firearm type. Any force component that misaligns the sights while squeezing is obviously bad and why handguns are harder to shoot accurately than long guns. Everything is about consistency when shooting accurately. Same grip, cheek placement, shoulder placement, pressures in each of those areas, trigger squeeze, etc. Even if you technically don't have great form or technique in some area, if you do it exactly the same each shot, you will be accurate (meaning small group size, not where the group is placed relative to where you wanted it unless you can adjust the sights to compensate). As the sage advice says, "Practice, practice, practice."
One exception to the above may be rapid fire. Very hard to work on a smooth squeeze and consistency if you must shoot fast for some reason, which is naturally why most people can't shoot fast very well (discounting effects from recoil). This shouldn't be a concern for normal hunting.
As Erik said, your biggest concern should be the break. It should be crisp and clean, no creep. A gunsmith should be able to fix that up for you. Even our competition triggers were somewhat mass produced so some could benefit from a polishing job. The typical firearm could certainly do so.
I'll add one more thing. Don't use a scope with too high a power. Just enough to clearly see that you are on target. The more magnification, the more movement you will see and most people have more of a natural tendency to jerk the trigger as the crosshairs are passing by the intended target zone. You can bump up the power a bit if you want once you've got better body hold technique. Or shoot from prone or some other "well rested" position.
I think this comes down to personal preference, your level of training, and what type of hunting you're going to be doing with your rifle. In general I don't think trigger pull weight is going to be the deciding factor as to whether or not you come home empty handed unless you are trying to snipe gophers from 500 yards.
According to an article in Field and Stream:
Good dangerous-game rifles have their triggers set at 4 to 5 pounds
That article opens up with a comment on a light trigger pull of 1.5 lbs.
... asked if that was a good pull weight for hunting rifles in general. To which I reply, great gobs of goose grease, no! Kenny sets his triggers light because almost all the rifles he builds are for carefully set-up shots at long range, and are purchased by experienced shooters who take the time and ammo to get to know their rifles.
They also say that there are after market triggers that can break cleanly at 2 oz, but most stock triggers won't function well below 3 lbs.
As far as whether a lighter trigger pull will improve your accuracy that depends. According to a forum M16 triggers are set to 8.5 lbs, and I've personally fired them accurately with iron sights at 500 yards. I'm not a terrible shot but I'm not exceptional either. I bring this up to point out that your estimated pull weight of 7 to 8 lbs isn't outrageous.
As this article written from a concealed carry pistol point of view points out a very heavy trigger pull can negatively impact your accuracy. They specifically mention double action pistols with a 13 lb first pull and special police Glocks with a 12 lb pull as very difficult to shoot accurately. They suggest a range of 4 to 6 lbs for your trigger weight which correlates well with the Field and Stream recommendation of 4 to 5 lbs.
Honestly what concerns me more is you saying the trigger doesn't break cleanly. I feel like you should probably let a gunsmith investigate that, and while they have the firearm ask them what they think about the current pull weight.
After finally purchasing a lighter trigger (3-4 lbs), I can say that yes, it does help one be more accurate.
It's much easier when you don't have to pull as hard, and the cleaner break makes it it much less jumpy when you go to pull.
It's also more enjoyable when you don't have to pull the trigger through a creaky break, and you notice it every single time you shoot.