Chris,
I have a 1960 26 footer, so I can give you a very close guess as to what
your 1959 24 footer will weigh. When my trailer is fully loaded and ready to
go it weighs in very close to 5000#. If you load your trailer similiar to
how I do ( a BIG IF ) your trailer will weigh in at about 4500 to 4800
pounds. This will be pushing the stated limits for your Blazer, but may be
OK. As for the trailer starting to sway at 50 mph. This is a classic symptom
of too little tongue weight. A properly loaded trailer will not 'wag' under
normal conditions at any speed normally seen in the USA. Get the weight off
the rear of the trailer and try to pack things so that more weight is up
front. Anti sway mechanisms are not built to compensate for an improperly
loaded trailer like you have. They are made to control sway induced by
things like passing semis and gusty winds.
While your Blazer may handle the weight, you will find that a vehicle with a
longer wheelbase will vastly improve your towing experience. Another option
would be to get one of the costly hitches. Others can give you names and
approx costs.
Scott