What's the worst that could happen? You could crack the hitch head when greater than normal stress is encountered (think of going through a swale or hitting a big bump). You could also have insufficient friction to counter the sway; a heavier TT needs greater friction to dampen unwanted motion, but you can't apply greater friction because of the hitch's limitations. So, I vote for a new hitch.
If you don't want to spend on a heavier Equal-i-zer, the Husky Centerline TS appears to work in the same manner but is priced lower.