What kind of harness are you using? The answer depends a lot on that.
If you have one where there is a separate neck loop and rib loop joined by a strap, then the tummy half should be quite snug but the neck part really doesn't need to be, one of the many reasons this kind (H-style) is better than the other. The collar half of this kind of harness is really only there so they can't slip out of the other half, so it can fit quite comfortably even loosely, just not so loose they can get their head out.
If you have the kind that is called a figure-8, in which the neck and rib loops are dependent on each other, you don't want to make it too tight because invariably they wriggle the rib one looser and the neck one gets tighter-- my main concern about that kind of harness. If you make it loose enough that it doesn't strangle them, they can get out of it. Well, some cats are less active and this kind of harness is okay, but if they roll around or run or really anything but just sit around or walk slowly beside you (HA!) then it's not the greatest.
I agree, definitely boneless-kitty syndrome is from the harness. Most cats do this at first. Have them wear it for supervised periods maybe an hour or so a day until they're used to it and act normal. It's helpful to distract them with pleasant things, a meal, playtime with a favorite toy, etc.
Some recommend getting them to associate the harness with being outside, it can't hurt but it'll happen naturally as soon as you start using it normally (ie, put it on, go outside, come back, take it off). So like, you could put it on in an open window or whatever-- I don't think it's really necessary unless your cats are former ferals or something.