First thing's first: I feel the need to define "soft science", since it's often used interchangeably with "social science", and social science is a much wider umbrella. For my purposes, the soft sciences include psychology, sociology, cultural anthropology (I consider physical anthropology a hard science) and possibly political science, if we happen to range that far. Conversely, the hard sciences are the traditionally empirical ones: chemistry, biology, geology, perhaps physics (although I'll admit, my grasp of physics is tenuous at best, so I don't feel comfortable putting it firmly in one category or another; it deals with forces that are measurable but in largely hypothetical situations and I don't know where that would go, and this is totally not a run-on sentence). So. Okay.
Hard sciences and soft sciences are both worthwhile, most of the time. This I'll happily concede, since I agree. And the so-called soft sciences are not invalid disciplines. They are often useful and interesting. Grabbing a couple classes in both sociology and anthropology was fascinating and while it does not make me an expert, it does make me more aware of the power that society and peers have, and psychology does teach us the power of our own mind. I can, in fact, think of several of my peers who would benefit greatly from taking the time to study human behavior in an effort to better understand social interactions. I'm not sure if it would make them better at it, but at least they would have a better grasp of what's going on and maybe be able to pick up on more social cues. Soft sciences have merit when considered as disciplines. However, they have little merit as sciences.
Ah, psychology. It's caught in the middle between science and pure discipline. We learned a lot from the original Stanford Prison Experiment, and we confirmed a lot of those lessons when the BBC repeated the SPE in 2000. We learned a lot from Milgram. Putting ethics aside for the moment, those were experiments in the human mind that were controlled, that were designed to prove or disprove an hypothesis. Milgram's experiment especially seems to embody the scientific method beautifully. But what did Jung learn from experimentation and not speculation? Psychology could perhaps be used in a more scientific fashion, but it seems like more often it's used in the fashion of a discipline, based on speculation and 'gut feelings'.
Sociology and anthropology (at least on the cultural side, as stated above) overlap in a lot of places, and they have a lot of the same problems when it comes to defining them as a science. The scientific method is very simple: hypothesis, experiment, data, conclusion. It's not just something for 5th-grade science teachers to torment students with. While sociology and anthropology are both very good at forming hypotheses - it is, after all, the easy part - they aren't so good at the rest of the scientific method. Sociology might, as a completely stereotypical example, form the hypothesis that youths in inner cities have a higher dropout rate because of external pressures such as gangs, family, and peers. Specifically (the hypothesis might continue), it's because academics are sorely undervalued in this environment, while the characteristics of a street-smart 'tough guy/gal' are far more valued. Ergo, the higher dropout rate in inner cities* is due to societal pressure and not necessarily due to lack of academic ability. But how does one prove that? By observation? Where is the control? One can certainly deal with statistics, but statistics are raw data, without a lot of context behind them, and the methods of gathering them can sometimes be questionable. (For instance, I have yet to run across a formal survey that didn't seem to be putting words in my mouth, at least a little, in how the questions are formed.)
Science is supposed to be the ordered search for knowledge and answers. It is not about the tools so much as the methods. Science is exacting, and as precise as possible. Scientists have developed many tools to facilitate this, but the tools are not actually the trade. Using your example of the Stress-o-meter, there isn't one and there probably is not one in development because it's not needed. We don't need psychology; we can isolate stress hormones to determine if someone is under stress, and compare it to a baseline in order to determine how stressed they are.
If we really want to get frisky, we could note down physical characteristics of stress and record them against levels of stress hormones. At 10 mg/mL of 'stressitol' (my made up stress hormone), the subject's pupils start contracting. At 20 mg/mL of stressitol, the subject will start visibly sweating and fidgeting will be more pronounced. Etc. Do this enough times across enough people and you start to get a baseline of how humans react to being stressed out. Most chemicals cause physical reactions in the body (such as narcotics causing the pupils to dilate) and this theoretical stressitol would be no different. If we pay attention, we can document the physical signs… and all without psychology or to much guesswork, and without trying to read the person's mind. Since stressitol is an alcohol, by the way, it obviously would be degraded into sugar, explaining the burst of energy during and directly after stress, followed by a sudden crash similar to the one experienced after a 'sugar high'. This is just one example of the things that can be explained with chemistry alone, without involving anything from a soft science.
I would venture to say that the soft sciences deal more with relatives, while hard sciences deal more with absolutes. The temperature of absolute zero IS 0 Kelvin. The rate of reactions, how much heat they produce, even the amount of energy required to overcome entropy and kick off a reaction - these are all quantifiable, measurable, definitive save for perhaps a little room for instrument or operator error. They are thus because past scientists have worked through the scientific method and placed values as accurately as possible on those things. In contrast, a lot of research has been done for soft sciences, but they deal more with "Is Jan feeling more stressed by this pressure than Jim?" and similar questions. It isn't that they are not valid, but the answers are not pursued in a scientific manner.
* I actually don't know off the top of my head if the drop-out rate in the inner-city is higher than that of the suburbs, and it's irrelevant right now. I just want to make it clear that I'm using that statement as part of my thought experiment, not as a statement of fact.