We had a similar dilemma. Given our current boat (Fletcher 19gts) is our first boat, when we were looking into buying, we spent a lot of time seriously considering having something just about trailer-able to save the c. £2k per year 'on/at the water' storage costs.
We knew we wanted overnight facilities on board, and the smallest/lightest boat would have been something like the Fletcher 19GTO. We both drive hatchbacks, so one of us would have had to have changed to a smallish 4x4 like a Freelander if we were even to stand a chance of towing/launching/recovering safely, reliably and legally. In addition, we both have post 1997 driving licences, so can only tow up to 3.5t combined train weigh (without needing to do a towing licence) so we'd have had to have been pretty selective with the actual car we chose.
With all this in mind, combined with the extra cost of running a bigger car all the time (fuel, tax, insurance, tyres, servicing - all adds up!) the costs of trailer upkeep and the greater hassle of usage of the boat, we bit the bullet and stuck her in a dry stack. In fact, the hassle element was probably the biggest factor which lead us to make this decision. If we had gone down the towing route, I expect we would only have used our boat half as much as we have done with her in a dry stack.
but I'm pretty certain that a 3.0l stern drive engine weighs about 400kgs
I'm prepared to be proven wrong here, but I think this estimation may still be a bit OTT. The engine is about 234kg and the alpha one leg + transom assembly is about 54kg, so 288kg combined. Add on the trim pump, and I expect you're up to a nice round 300kg.
Anna will no doubt put you right on that sees

Yep, 1370kg fdry weight for the 19GTS (sterndrive versions).
What I find crazy is the fact that if you take the dry weight of an engineless GTO vs an engineless+driveless GTS, there's 220kg more weight in the GTS' hull (GTO = 850kg and GTS = 1070kg). I have always assumed this is because of the additional internal hull structure required to accept the inboard engine mounts in the GTS vs the GTO spec hull. Also, the GTO is only rated up to 150hp (or is it 130?) IIRC, whereas the GTS is rated up to 245hp., which I presume commands a stiffer/stronger transom.
We have a twin axle SBS trailer for ours, and I expect, with everything included (fuel, fluids, junk etc) on the trailer, we're looking at around 2000kg.
With all this said, I do agree with NickT though, that if you have a suitable vehicle, then a Fletcher 19GTO could be perfect. It just sounds like you will struggle a lot if you try and launch and (more crucially) recover with your present car. But then, if you do end up having to change your car to safely launch/recover, then why not just choose somethig that'll happily launch/recover a a GTS, such that you're not just limited to a rare breed of boat? Don't be too put off by the servicing costs of the inboard either. It's easy enough that even I have been able to keep ours running for the last three seasons! I'd say average £250/year (if you DIY) to cover standard servicing and a bit of preventative /ongoing maintenance. Some years will be cheaper, but some more expensive - like this year for us, where we have to do manifold+elbow, gimbal, bellows, carb rebuild, service and a couple of other bits - but it's just bad luck that its all occurring in the same year! It's certainly going to put my mechanical skills to the test!