Why does Ann get offended when Carl asks her if she's size four?

By asking for her weight, it implies that he is interested in her body which makes her uncomfortable. Earlier in the film, we know she is struggling for her work. She is recommended to go to the burlesque club in the script:

Weston: Look - I know times are tough. You want my advice? Use what you got. You’re not bad looking - a girl like you doesn’t have to starve.

HOPE flickers in ANN’S EYES as WESTON fishes into his POCKET for a PEN and BUSINESS CARD. He scribbles down an address.

As she reaches the burlesque club, she realises what it is and is disgusted:

CLOSE ON: ANN ... standing in the MIDDLE of the SIDEWALK. She is unaware of DENHAM watching her. ANN stares grimly at the BURLESQUE HOARDINGS, the FLYER clutched in her hands, a small knot of anger forming in her stomach.

CLOSE ON: DENHAM’s HAND lets go of the DOOR. His eyes lock on ANN through the sea of PEDESTRIANS.

ANN angrily CRUMPLES the FLYER, drops it in the GUTTER and walks away from the THEATRE.

She leaves and steals an apple given how hungry she is. Denham sees this, pays for it to avoid her getting into trouble and offers her a hot meal. This is obviously exactly what she wants - then he asks about her size.

Understandably, she is concerned that he is effectively bribing her with food in return for something (such as work at the burlesque club). As her feelings earlier showed, she is deeply angry at the idea of working here and so begins to storm off.

He then calms her by reassuring her he is casting for a role in a film, not trying to make her dance or do anything else she would feel uncomfortable with.

Size 4 means Extra Small, below is the full chart of woman size from tactics.com :

Asking woman's size is obviously for the reason of this reaction and even calling her size 4 (means "smaller assets") is also offensive.

In the context of the scene, it seems to me that the question's context is different from the other answerers' interpretations: the actress who was going to play that part backed out after they bought her wardrobe, so if she were the same size, it would save them money. He thinks so little of her, or expects to pay her so little, that this small fact is significant to him.

At least, that's what it meant to me when I saw it. Only a little of it is stated, but to me, it was all implied.