What was wrong with this tube?
 

When pumping up my rear tire, it would get to about 60 psi and then I couldn't pump it up past that. It would go up and then right back down. I tried tightening the presta valve core and tried a new core but that didn't work. I put in a new tube and was able to pump up to 100.

When I pumped up the old tube, it didn't keep a round shape. Also certain parts got very wide and where the valve is stayed skinny.

What causes this?

The tube is not really meant to be inflated hard without a tire supporting it. The valve area and seam areas are going to be thicker and produced different stretch abilities. If pressurized too much those differences can stress and potentially rip or leak. It is possible the tube you are referring to may be old or have a very minor leak that expands only when pressurized to that degree.

That makes sense. Hmm maybe it had slow leak. Sometimes when I go over 60psi it would really start blasting out. Anyway thenew one is working and I threw out the old one. I should have used soapy water to check for a leak.