At 3500lbs, a weight distributing hitch is not strictly necessary and I personally believe that sway control arms are more of a band-aid than a cure. Make sure the car's suspension is in good shape and make sure your tongue weight is around 10% of the trailer's weight.
That said, a weight distributing hitch will not cause the rear of the car to sag -- just the opposite. It transfers some of the tongue weight from the rear axle to the front, which tends to lift the height at the hitch. This leveling of the car has the benefit of reducing any tendency to sway -- the rear axle is much less of a pivot point and the front wheels have a firmer grip to keep things in line.
I will also mention that most North American jurisdictions require trailer brakes on at least one axle if the gross trailer weight exceeds 3,000 lbs.* so if you are towing 3,500 lbs you should probably have electric brakes installed. In the event that you run into sudden and unexpected trailer sway, such as from a sudden crosswind, a touch of trailer brake from the manual lever on the controller can help steady it down before things get out of hand. Don't Ask Me How I Know This.
*There are exceptions, one or two don't require it at all, some have a lower weight threshold, some require brakes on all trailer axles..