Recently, I've noticed that I attract a lot of insecure girls. Girls that say things like:

"I'm not that pretty, I'm average at best."
"I don't like my face."
"I'm chubby"

etc.

How do I respond and hold an attractive frame when a girl says an insecure comment about herself? Do I try and ignore this?

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When you do the right thing, you will be shocked at the things that will happen in return. When you do the right thing, it always comes back.

What I've done before when a girl says she's fat is play along with it. I'll be like ya me too I need to go on a diet look at my fat disgusting belly. I am in top shape and ripped the girl I say that to is usually like shut up in a joking way or I wish I was fat like you just to kinda lighten the convo. Its worked great for me in the past. I had a girl one time say she hated her nose I was like ya I really think you should get a nose job. In a sarcastic tone she hit me and was like you're real nice, but the effectiveness of responses like that are based on the delivery of the response.

i’ve met a few women that say this, but only after a while i first met them, so during like a few weeks of relationships. i have never met women to tell me that they are insecure at the beginning, because they are afraid to put themselves lower so that i do not leave and make relationship with me, i suppose. but during relationship women said it to me.
at what stage do they say it to you? during relationship or at the beginning?
if it is during relationship, just go single.
How do I respond?

Insecure statements can mean many things, each one warranting a different response:

-she may be testing you to see how 'hooked' you are by your response
-she may be testing you to determine what type of guy you actually are (e.g., coddling, cold/asshole type, etc) to determine the frame of the relationship, especially if she's allowing you to set that frame which many girls are
-she may just genuinely feel insecure/unattractive and wants your validation (in which case its never enough to allay her insecurities - this requires her to do some work, you can't 'fix' someone)


To take the safe route you can query her "why do you feel this way about yourself?" without addressing directly the specific flaw she is mentioning. This may help her get to the core of the insecurity rather than its surface, physical manifestation ("I have a big nose" - which really has little to do with her nose at all but rather self acceptance).