Actually I thought if I could reply on SG readings it would be quicker and easier. Maybe this isn't the case.
Hi, I've read about a zillion specific gravities on photo chem samples, but they won't be much help in your situation. For the most part, a sp gr reading tells you the general weigh of chemicals dissolved in water. So if you mixed a developer wrong - perhaps the wrong amount of water - there would be a change in the sp gr. But for you, since you are mixing it yourself, it's easier to just double check that the amounts are correct. Now, if you sometimes use different dilutions of HC-110 and forgot which one it was, then a sp gr could help figure this out.
With respect to determining if a developer is still good, sp gr is of little use. For example, you could destroy a developer by bubbling air through it (this would oxidize the developing agent, ruining the developer), yet the amount of dissolved chemicals, and thus the sp gr, remain essentially the same.
By far the best way to check the condition of a developer is to develop a test sample of film or paper in it. In commercial work you'd want to have a densitometer and some sort of known-good reference, but for your own work, your eyes are probably just fine.