Unless the work you are doing is really good for your career, finish your schooling and get a full time job.
First off, you do not want to have to split your semester for two reasons: time and money. School is really expensive, and you don't want to have to pay for an additional semester.
Next ask yourself is the experience you will be gaining from staying is going to be extremely beneficial for your career. You have already worked there for the summer, will working there for another 4+ months make your resume significantly stronger? If you are in a situation where your resume is not strong enough to get you a job upon graduation but staying at this job longer will tip the scales, maybe think about staying, otherwise move on. I don't see a situation where this could be the case, you never know.
There are other options too, for example you could try asking for a full time job at the company upon graduation. This is pretty common in my school's internship program, with the majority of people getting job offers upon graduation. In your case, you might not want to consider this option unless they give you a rather large pay raise. It is not the purpose of this question, but try looking up online what is the standard pay range for the job you are looking for so you don't end up dreadfully underpaid.
ps. Your assumption about being paid better
is should be correct...