I've had that exact problem a number of times. It's normally (Thanks RamblinRev) a top-tension issue. i.e. Not enough...
Though needles appear to be sharp, buy new ones--made a big difference for me.
Also... when threading the bobbin in the carrier, the thread should feed opposite of what you'd think.
You normally don't have to mess with the lower tension, but I did in order to make it work.
With the bobbin in the carrier, suspend the assembly by the thread. It should hang still. A slight movement and it should release some thread. If you are going to play with that, tighten only 1/8th of a turn at a time. It's a sensitive adjustment.
I found that bar-tacks often cause bottom tangles, but going slow and raising the tension helps a lot. I bought a cheap pack of singer needles at Joannes, two orange, two blue and two purple coded. (red top for woven fabrics)
Orange: 11, Blue 14, Purple: 16.
I use the orange ones for all fabric sewing.
For making loops in straps, I use heavy-duty thread and #16 needles.
For grosgrain, if I'm having issues with bottom tangles on bartacks, I found the #14's to work well. (going slow helps)
Once the machine tangles, I pull ALL the thread out, remove the bobbin and start over. Sometimes I've found the machine will spin the main spool, causing a loop of thread to go under the spool and wrap around the shaft. That generally ends with broken thread... The bobbin can do the same thing...
Don't forget to get some good oil, and follow the instructions for lubrication. Here's the manual and machine settings guide, if you don't have them:
BTW: you have to pull one screw to lubricate most of the machine, and the sewing plate should be pulled and the feed dogs cleaned. It's not a great machine, but I've made LOTS of stuff with it. It's a bit temperamental, but for $35, I can put up with some quirks...
Hope this helps. If you need more help with that specific machine, PM me and we can talk in person. (though I'm NO expert at sewing... I just know my machine)