Handye9 has an excellent post! A few more things I can think of. Depending on age of TV, check for excess play in front end & steering. Also check for excess play in receiver/hitch (Reese for ex. has shims available). Shocks on the trailer can help and depending on age again, the TV may benefit from new shocks, esp. some good HD ones.
As Barney says, tires are another important factor. Going up a load range will give you a slightly wider tire and higher pressure rating, both of which will help stability, sway & handling. The higher load capacity rating really helps to minimize the risk of a premature failure too. Keep your ST tires inflated to sidewall max. psi and check them routinely (cold).
