The main problem you are experiencing is that the sideways force from the angled blade is acting to push the tractor sideways, overcoming the straight forward push from the wheels. Have you tried a different approach angle? If the blade is set at more of an angle, the division between forward and sideways thrust will be different and you might find it will work just fine. You could also just leave the blade square for the first pass, then make a second and third pass to push things to the side after you can get more traction in the middle of the drive. It all depends on the snow you're pushing.
Snow is funny stuff to move around. Sometimes it's light and fluffy and moves easily, sometimes it's like thick mud. The traction you can get while plowing varies a lot.
I think if I was you I would look at chains on the tires before weights. Granted, you may need to be careful when turning, but you'll get more traction from chains than from more weight on hard pack or ice. I think chains for the front may be cheaper than weights, too.
Another option is to spend less money and get a back blade (or use one you may already have) for the first pass and the front blade for the more delicate precision parts of the job. I lived over by Muskegon in serious snow country for several years. I had flat ground and plowed my snow with a rear blade on an 8N with unloaded Ag tires and no chains. I had no problems moving considerable amounts of the stuff. Again, the ground was flat, I had lots of room to work in, and didn't worry about the lawn and such. To put it in perspective, a lot of people over there plowed out their whole yard at the start of winter. I asked why, and they said it was so in case of a "good ole Michigan winter" they would have enough room to pile all the snow as the winter progressed.