just so we use the correct terminology.
sounds like what you have is a WDH, weight distributing hitch. not sure what brand you have.
Equal-i-zer is a brand name for an American-made WDH that has built-in sway control. since it has built-in sway control, it doesn't need friction bars like the chain-type WDH's. it doesn't have "stabilizer bars".
it's so well loved, it's become a common term for a WDH. sort of like Kleenex for any brand of tissue.
and Zoe the Wonder Dog(R.I.P.)
'07 Roo 23SS pushing an '07 Chevy Avalanche
Equalizer WDH and Prodigy BC