I have seen many incorrect tabs and chords for this song on the Internet and I've had requests for it from some of my students. The chords are easy enough, it's mostly the picking pattern that is a little tricky. But once you get the hang of it, the fingers should just roll through it.

If you like classical notation, the right hand fingering on the patterns below should be: m p a m p i

"The Weary Kind" - Ryan Bingham

From the movie "Crazy Heart" with Jeff Bridges
Chords and Tab

Figure 1

Picking pattern: This is a two-beat pattern so play each pattern twice to fill one whole bar.

D                           A
|--------2-----------|     |--------0-----------|
|---3-------3--------|     |---2-------2--------|
|.---------------2--.|     |.---------------2--.|
|.----0-------0-----.|     |.----2-------2-----.|
|--------------------|     |--------------------|
|--------------------|     |--------------------|

G                           Bm
|--------3-----------|     |--------2-----------|
|---0-------0--------|     |---3-------3--------|
|.---------------0--.|     |.---------------4--.|
|.----0-------0-----.|     |.----4-------4-----.|
|--------------------|     |--------------------|
|--------------------|     |--------------------|

Figure 2

In the chorus, the chord A7 has this common variation. Use the same picking as figure 1, but each of these chords gets only half a bar, so the whole sequence of four chords fills two bars.

A7:      x02020
A7sus4:  x04030
A7 (v2): x05050
A7sus4:  x04030