Weaker signal WITH wireless repeater.

While a repeater will work most of the time, it's not a guarantee. It all depends on the nature of the problem. A repeater typically helps, but that assumes the problem is, in fact, range. Let's take an extreme example to illustrate how that might not be the case.

Suppose a highly dense wall lies directly between your wireless client and the wireless router, something that almost no wireless signal could penetrate (maybe LEAD, just to be extreme). It isn't going to matter all that much if you use a repeater directly between the wireless client and wireless router, even if that repeater is a mere 3 ft outside that wall. Your problem isn't range, but rather the obstruction. If you're lucky, the obstruction might only exist in one direction. And by placing the repeater FARTHER away from the primary router, but in a direction that's allows the repeater’s signal to come to your wireless client in a direction AWAY from that obstruction, you might get a better signal.

Yes, it all sounds counter-intuitive. How could increasing the distance between the devices improve the signal. But again, if the problem is not range but obstructions, then what really matters is LOCATION/PLACEMENT, not distance. In that case, you use the repeater to alter WHERE the signal is coming from, even if that increases the distance the signal has to travel. Of course, the repeater still needs to be within reasonable distance no matter the location. You can only push this so far.

In your case, when floors come into the picture, you typically don’t have as many options when it comes to placement. Not unless you can find a location where perhaps the floor is thinner, or perhaps not obstructed by rafters, or perhaps near a basement window.

If all else fails, you either have to consider placing the wireless router on another floor, or else use some other technology. For example, it might be better to use power line adapters to run the signal from the router up to each floor, then drop WAPs (wireless access points) on each floor. That way, everyone gets a strong signal. IOW, you use the power lines in your home/office as a wired backbone (I’m assuming you’re unable to run Ethernet wire, but if you can, that would be even better) rather than trying to FORCE wireless to work under circumstances where that just isn’t possible.

Wireless has its limits. You can’t solve EVERY situation via wireless. Sometimes it takes a hybrid solution, like combining ethernet/powerline and wireless, as I described above.