A "balanced" stitch has the threads interlocking between the fabrics, with neither thread showing on the other side. And, the tension on both is adjusted so that the seams lie flat with no pulling or puckering.

Can you show a picture of your problem?

Thank you for your interest. I am uploading two photos. The first one is the underside of the work showing the pink bobbin thread and the little dot of black top thread. The numbers indicate the top thread tension dial. I sewed a line, then turned the top tension one number and sewed another line and repeated.

Please for give that this sample is on a printed fabric. I never thought about taking pictures....but I am new at getting sewing advise from the internet. I will redo this on white or cream if needed.

The second photo is of the top of the work, showing the top black thread. The stitches change VERY little with each movement of the top tension. I would think there should be more noticeable changes.

Here goes.....I hope I can get the photos right!......well I have tried,and don't know how to get the orientation correct. Perhaps you can tell anyway.

There may be lint build up between the disks of the tension mechanism.

Cleaning the machine can't hurt. It's amazing how lint builds up.

I would start by adjusting the bobbin tension:
https://www.superiorthreads.com/education/bobbin-tension-adjusted/ 
When it is set, it seldom needs adjusting again, just checking.

Then turn the upper tension as tight as it will go, then loosen it 5 full turns. Test it by sewing a few inches.

Go tighter or looser by 1 number if you need to, check it again.

http://www.threadsmagazine.com/item/4302/understanding-thread-tension 

Thank you for your help. I have taken the covers off and oiled every metal gear and rotation point. I have completely cleaned all the lint out from the machine and bobbin areas. I spread the tension discs apart, and made sure it was clear between the discs.. I am convinced that machine is cleaned and lubed better than if a technician had done it, because I had more interest and time to work on it.

I bought two new bobbins....neither made any difference but I am surprised how tight they are.....the won't drop the bobbin at all (or very little) with a snap of the wrist.

My big question is the needle plate is chewed up. (Lots of broken needles over the years I guess....I do mostly home decor sewing with heavier materials) I will attach a picture. Do you think it is possible my bobbin thread is catching on this messed up needle plate, causing my tight bobbin thread?

After reading further, I do think this would be worth replacing...as the article referred above by lazy_gardens in "threadmagazine.com" mentioned the needle plate could cause problems. BUT.....how can I find this needle plate. I have scoured the internet for an Euro Pro 7130 needle plate to no avail. I have taken pictures and measured my needle plate, but none of the websites give the measurements of their needle plates. It looks most like the Singer V620033001, but I'm not sure because there is no measurements.

I have one more suggestion. Try taking a stiff pin and picking under the metal band on your bobbin case. There may be a build up of crud there. This is the same metal band that you place the thread under when changing a bobbin.

(It seems as if your bobbin thread has little tension rather than your top thread being too tight.)

You could also try removing it and checking there, but be aware... that screw is impossibly tiny and must NOT be lost. I work over a large magnet when doing this type of sleuthing.

Actually, there are TWO screws... the tension screw and the attachment screw.

Thonotorose, Thank you for helping. I have bought new bobbin cases to eliminate the case as the problem. The new cases made no difference, except to surprise me at how tight they were set from the factory. The bobbins drop very little if at all when I do the quick reverse test. I have played with the bobbin tension many times through the years, and have always set my bobbins looser than these new ones that just came in. I tried the new bobbins at both the factory setting, and at a looser setting.....the results were unchanged.

I thought my bobbin thread is too tight (or needle thread too loose). However, not matter how high I set the needle thread tension, the needle thread still peaks out underneath my project. This makes me think it MIGHT be the nicked needle plate catching the bobbin thread causing it to have too much tension? It seems to me the bobbin thread should come up in the center of the needle plate and never even touch the sides of the (zig-zag) opening. But I don't really know.

The needle plate can be smoothed out. You don't need to get a new one.

That only causes fraying or breaking thread, not a tension problem.

I'm not really seeing any problem. Are you changing your needle and using different sizes depending on what you're sewing? They can get dull after a while. Also, different fabrics and thicknesses need different sizes.

The only row that looks really bad to me, is the first row.

You can smooth out the snags on the needle plate with a small metal file or some of the sandpaper strips plumbers use to clean pipe with ... or both.

It may not be the problem, but it's not a good thin

Not a technician, but would like to add that thread can be a factor in these sort of problems as well as how the bobbin is wound.

Tho I also wonder what the stitching would look like if both threads were the same?

And are you positive that you have threaded the upper part correctly & that the needle is inserted properly?