No, sway bars do not affect tongue weight. Right now, how much does your TT weight fully-loaded? What is the loaded tongue weight?
According the the
specs for your TT, it has a GVWR of 6,000#, w/ tongue weight of 610#. Now you can calculate the effect of adding 225# of bikes + weight of carrier to behind the rear bumper, and how it will affect tongue weight, as well as your loaded trailer weight.
Tongue weight must be a minimum of 10% of loaded trailer weight; 12% is better IMO.
FWIW, It's my experience, as tongue weight % decreases, sway increases-to a point..
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2000 Winnebago Ultimate Freedom USQ40JD, ISC 8.3 Cummins 350, Spartan MM Chassis. USA 1SG, retired;PPA,Good Sam Life member,FMCA.
"We the people are the rightful masters of both the Congress and the Courts - not to overthrow the Constitution but to overthrow men who pervert the Constitution." Abraham Lincoln