Pretty much what MGS said. I use a sewing pin through both lines where the loop starts, I actually use this and not pen marks. I place this at exactly 90 degrees to the line. I merely need to align the line and pin at 90 degrees when under the sewing foot to know the line is lined up 100% as I measured it. This has very very accurate results. Start your sewing on the pin or near it, making sure not to hit it. Apply tension to the loop and the 2 tails to get the sewing pin at 90degrees under the foot. Tension the loose threads and start the first few stitches by turning the machine by hand. If the pin moves out of alignment you can tweak it a bit and do a couple more stitches. After a few more manual stitches you can go automatically with the peddle as the line will hold alignment. As you work down to the end it should all pull together perfectly, stitches falling near the middle of the line. Now depending on you stitch length and skill you can either reverse back up the line or release the foot with the needle DOWN, rotate the line and go back over the end like that. You can do this 3-4 times if you have a long stitch width or not at all if the stitch length is short like on original pulley lines. ALSO and important I like to apply tension usually always to front and back of what I am sewing, the shitty machine I have just can't seem to cope(no adjustable foot tension:-/) This can require some skill as you need to move both hands in sync with the stitches to get nice even spacing length wise.
Setting the machine up can be a bit confusing at first. The orientation of the bobbin spool can change the bottom tension, the top tension should be adjustable if it is not or if you can not get it tight enough you can wrap the thread around something. Proper top and bottom tension is with the threads meeting hidden in the middle, you can see this looking at the top and bottom after you have sewn a bit. In reality if the tension is more to one side with one thread more on that side and it will still work fine so don't worry too much about that. What tension can do though is affect how nice the stitching is, so play with it till it works best you can get it. As to the stitch type and width look at what is used on the kites and lines etc and just copy that. Once you have worked out the best settings I like to right them all on the side of the machine with a short name for the stitches use, like kite seam, line splice, kite join, sewn end etc with A3 T5 A(stitch type on my machine) 3(length and width basically size) T(tension) B4T9 etc.. This will save immense frustration as the best settings can take a bit to find, especially if you only do this a couple times a year.
Lastly I have modified my sewing machine by removing the free end cover and lamp, which gives a lot more freedom to see what is going on. I then use a high powered headlamp to see what I am doing which is much better than the shitty lamp in the machine. Not really applicable to just doing line ends although it is helpful, but when you try to repair a foil kite you may wonder how the fuck anyone does it on these little machines and in truth they don't, they use many $1000's expensive long arm machines, with so much space you could park a car in there.
And lastly lastly, your thread looks a bit thin, although you can make it work with lots of stitches. Go into a furniture repair supplier and buy a multi kilometer spool of nice nylon thread, take a kite or line to match the thickness as best they have, it sounds expensive but they truly cost peanuts and the roll will last just about a lifetime and you can use it for all sorts of things and the thread will be of a much much higher quality than the shit from a craft store. Nylon is about 1/3 stronger than polyester. If you really want to go crazy you can use dyneema fishing line, like off ebay, but that may not be great for fabrics as it could cut through it , for lines and bridles I read it is the best though.