Same way I always have, as I refuse to haul around more than one suitcase + a daypack. Of course, I've never been in a situation where I was staying in one place for a couple of months, so in that case 2 bags make more sense.

Anyway, I use compression bags to squash everything nicely, then add a cloth duffel on top of the bag. When I reach check-in, I pull out a few of the compression bags and put them in the duffel, then check them both. When I arrive at the other end, I re-combine them. Most of the time the fee for an extra bag will be less than the fee for an overweight bag, should it come to that.

BTW, a tip for making sure of test-run weight. Take your bags to a veterinarian's office; they tend to have nice big floor scales that are used to weigh dogs, and I've never had one refuse to let me use it to test my luggage.