Another golfer, with a member name of A.Princey, has asked for advice about his woods potentially being too light because he has been struggling with them compared with his heavier irons. And as is frequently the case, he has received horrible answers from so-called experts on the Worrisome Reasonless Xenogolf forum website, a site that continues to contribute to the declining participation and reputation of the game of golf with many of its wholly incompetent answers as presented by supposed golf experts. In this case, responses broadly recommended making sure that shafts are ascending in weight when going through a set of golf clubs, a ridiculous concept (yet another one by the clubfitting trade). But I will help out A.Princey just a bit here.
First, for those for whom swingweighting works, the only relevant club value is the swingweight of the golf club, while the total weight of the club(s) can generally be ignored. This is the whole benefit of swingweighting, where a golfer can make equally good swings when switching among clubs that otherwise vary in their lengths, total weights, shaft flexes, grip sizes, and more. But stay aware of my statement saying “for those for whom swingweighting works,” because it does not work for everyone. Its 14-inch fulcrum dimension broadly tends to become a better fit for golfers as they play and practice more over a longer period of time. So among other things, you need to specifically learn where that dimension is derived from and how well (if at all) it fits you personally. I would actually have to see you make a few swings in order to determine whether swingweighting works for you and determine what to recommend if it does not.
With that said, by your description you certainly do appear to have one or more errors in your clubfitting between your woods and irons. I will start by saying that if the clubs were fit well to you, you should have no trouble switching between clubs that are lighter in total weight and clubs that are heavier in total weight and swinging them both equally well (regardless of what shaft weights are in any of them). In assuming for a moment that swingweighting works well for you (but it may not) and your swingweight values are matched between your irons and woods, there is somewhat of a good chance that your grip size is incorrect on your woods (assuming that your irons fit you properly, which they may or may not). If you are like most golfers, and regardless of the method used to initially fit your grip size, it is a fatal clubfitting flaw to simply keep that grip size the same on all of your clubs.
As clubs get longer and/or lighter, larger grip sizes will be needed in order for you make your best swings when switching between various clubs. This is really first-grade-level clubfitting knowledge. In going back more than 50 years, wood shafts have frequently been made with larger butt sizes than iron shafts. This is not done to inconvenience golfers and make them scramble around for various grip core sizes to put on their clubs. There are legitimate reasons for it. Shaft designers with appropriate knowledge would presumably try to account for this, but in many other cases they might not and you are totally on your own.
Now if you really have a firm belief that all of your grip sizes should remain the same among all of your clubs regardless of what all of the other club specifications are, then I would agree that shaft weight becomes a more important element (heavier shaft weights if the grip size is too small [for your swing] and vice versa). This is called fitting your shaft weight to the existing grip size and is commonly the way the clubfitting industry operates. While more convenient for the trade, in the end it is not correct and generally limits how low you can go in shaft weight. But when fitting your grip size to the existing shaft chosen, there is (theoretically) no limit to how low you can go in shaft weight and still swing well. To illustrate, you should be able to form your hands together and swing as well as you are possibly capable of with no golf club whatsoever in your hands (this is the whole purpose behind the concept of overlapping or interlocking gripping structures in golf), and that is a condition of absolutely zero weight being in your hands. Thus, if you cannot achieve that same quality of swinging with any weight shaft in your hands, then there is at least one notable flaw somewhere in the clubfitting process.
But the garbage about you potentially needing ascending weight shafts in the other responses you received is just that, garbage, and you should totally ignore that nonsense. While you clearly lack some rather basic clubfitting knowledge that is hurting you, it is nevertheless nowhere near as complicated a process as many (if not most) others make it out to be, so do not get discouraged. To cite a couple of very common issues still very rampant within the clubfitting trade (which is still in its infancy in certain ways), the “mysterious” golf shaft tends to be a much more important clubfitting component and variable among people who lack crucial knowledge in other clubfitting areas (such as though not limited to the above). But the better certain other foundational clubfitting elements are understood, the less critical the shaft generally becomes in nature (which makes perfect sense).
Another current issue has countless self-proclaimed clubfitting experts like Howard Jones somehow believing that MOI golf club matching is some sort of improvement or advancement of traditional swingweighting and continuing to promote the absurdity. But the two specifications are essentially complete opposites of one another in both theory and practice, with MOI being better termed Moment of Insanity as a golf club matching concept. Many such people are largely book-taught clubfitters with somewhat limited actual playing experience (with performing experience beyond just golf also potentially being quite valuable) and thus have little other choice but to blindly believe what they hear and/or read from what turns out to be various other clueless people.
Many such people end up on the above noted and similar forums, with paying sponsors being given far more posting privileges and such sponsors frequently being the least knowledgeable of all regarding certain golf-related subjects. So if you seriously listen to the advice regularly given out on the above-noted and other similar golf forums, you might be encouraged to abandon the game like so many others have in recent years, and rightly so based on the replies that you and so many other poor golfers have received.
I know this does not answer all of your questions and might even raise some new ones for you, but it should at least help to put you on a much better path than the delusional replies you got to your original inquiry. Good luck.