From the style of front tire, I'd bet you have 4wd, Look at the front axel and see if you have a driveshaft going back to the transmission.
If you are carrying a hitch borne implement, and you back up the hill then all of the weight on of the implement will be on your back wheels. However it will also take the weight of the tractor and put it on the front wheels. Try backing, and look for the 4wd. Reverse, low range if you have it, and 4wd will walk that hill.
Tossing weeds on that slope will just give the tires somthing to push out of the way. /forums/images/graemlins/grin.gif Wont hurt or help.
I would NOT repeat NOT place boards across that slope. When they get wet, you WILL slide. Honestly, that slope doesnt look all that bad, as in, you should be able to climb it with the tractor.