Car wobble

Car has a mean wobble (side to side) during mild acceleration (traffic) in first gear, up to about 30 mph, feels like it is coming from the rear of car. I am on original rubber in the rear with about 50k, so it is due for two new tires and balancing, could this be the cause?
Definitely feels like something is not balanced, are there any other parts such as drive shaft, manual trans, or differential causing this?
 
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Out of balance is more of a shake and usually at higher speeds than 30 MPH. Wobble (side-to-side) can be caused by uneven tire wear and/or failed belts where the tire no longer runs true. Do you feel the wobble in the steering wheel or more seat of the pants? You should have this looked at by a tire shop ASAP - although you don't feel it as much (or at all) at higher speeds doesn't mean that there isn't a problem. Obviously, you wouldn't want a tire coming apart at freeway/highway speeds. By any chance have you smacked a curb lately?