be, feel, look, seem
become, wear
The fabric was wearing thin.
That joke is wearing a little thin. (figurative)

extremely, fairly, very, etc.
incredibly
a little, slightly, etc.

be, look
become, get, grow
stay
How do you manage to stay so thin?

extremely, fairly, very, etc.
She's tall and rather thin.

dangerously, painfully
The old horse was painfully thin.

be, look, seem
The paint looks a little thin.

become, get
Be careful that the mixture doesn't get too thin.

extremely, fairly, very, etc.
a little, slightly, etc.

be, seem
The evidence seems awfully thin.

become, grow, run
My patience is running thin.

remain

extremely, fairly, very, etc.
dangerously, perilously
The team is dangerously thin at wide receiver.

spread sth (too) thin, stretch sth (too) thin
You can spread yourself too thin, often leading to poor choices.
His management team was stretched thin.

thin on the ground (BrE)
Jobs were still a bit thin on the ground (= not many were available).

thin on top
He's getting a little thin on top (= losing his hair).

Thin is used with these nouns:
air, arm, atmosphere, beam, belt, blade, blanket, body, build, cardboard, chain, coat, coating, consistency, cord, cotton, cover, crack, crust, deposit, disguise, duvet, eyebrow, fabric, face, film, finger, frame, haze, ice, jacket, jumper, layer, leather, leg, limb, line, lip, liquid, man, margin, material, mattress, membrane, mist, moustache, mouth, neck, needle, nose, paint, paper, plastic, ribbon, sauce, scale, scar, shawl, sheet, shoulder, shred, silk, skin, skull, slice, smile, sock, soil, sole, soup, stem, stick, strand, strap, stream, strip, stripe, stroke, sweater, thread, trail, trickle, tube, veil, veneer, voice, waist, wall, wire, wrist