I planted this peach tree 2 springs ago. It was about the same size when I planted. It bloomed each spring but failed to grow bigger. This year it bloomed again and I assume it will still continue to not grow. Is this simply a bad peach tree? I'm about to dig it up and start over with a new one. FYI - I have 1 other peach tree, 2 pear trees, and 2 plum trees also in the backyard that were planted around the same time and are growing great.

It looks exactly like mine when 2 years old, planted same as yours.
As always in my clayish soils, it's the thrid year the roots finally give the big boost to all that exposed, be it my peach and many other tree types unless they were 30+gal container (+esp. if pro-installed).

So my call is this looks healthy, growth is SOP for locals and things should be improving from this year on.

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Hard to say, but I had a Belle of Georgia planted out here in Midland about the same size as your tree. The first year it put on a little new growth, but the second year it really took off. Three years would be concerning to me, but the tree looks healthy to this point, so not sure.