the hitch itself flexes at higher speeds and causes the back end of the bike to wobble.
It's a squared hollow metal bracket that I'm thinking I could fill
ok,, without a picture,, I am guessing at the other 990 words [a picture is worth a 1000 words..]
but you mention it is a square tube hitch, and it flexes .. but you want to fill it..
that leads me to think the hitch doesn't flex per se.. but it has some loose fitting tolerance... and that allows the attachment to "rattle" or wobble,, as such .
Thule makes receiver square tube hitch attachments that "bolt" in.. instead of the normal standard pin and hair clip ...
when you bolt the attachment to the receiver it becomes quite stiff..
so if you can get a nut inside the attachment, and a bolt thru the receiver, you might find it stiffens it up quite a bit.
or , you might be able to thread the attachment , but I doubt that tube is over 0.250" ,,, which isn't really adequate.
you can make up a large "weld nut" from a flat bar that is sort of press fit into the attachment..
or you could just slip a weld nut in and weld it..
muffler shops can put a spot of weld on pretty quick and inexpensive if you need welding..
some reason I can link to pics ... but try this link
it shows a threaded pin,, but a bolt works just as well..
https://www.etrailer.com/static/images/pics/8/5/853-5917_1000.jpg
curt has something similar
http://ep1.pinkbike.org/p4pb7591933/p4pb7591933.jpg
http://www.pinkbike.com/news/Tech-Tuesday-Removing-Bike-Rack-Rattle-2012.html
Kill the klunk: While there are a few great bike racks available, not many incorporate any type of anti-rattle system into their design. Having your bike rack, especially one that's fully loaded, shake and rattle as you drive has to be one of the more annoying things in life. Not only does it make your vehicle sound as if it's about to fall apart, it also seems to get worse and worse over time. There are a few different ways to eliminate that clatter, but we're fans if the threaded insert design that the Curt unit shown here employs.
The Curt anti-rattle kit includes an insert that fits inside the rack bar, a threaded hitch pin (
bolt) and a safety cotter pin. When the insert is installed into the rack bar, threading the hitch pin into place sucks the rack up against the inside wall of the receiver.
more..
drill a oversize 3/8 hole in the bottom of the receiver an inch or two forward (toward the front of your truck) of the locking pin. weld an external nut over that hole.. and and tighten a 3/8 bolt to put pressure on the rack
Or just use a nail and pound it into one of the corners