Is weight a good indicator of bad health?

I recently from a fairly average weight (145lbs) to something that I consider more ideal (120) at 5'5. I want to lose some more get down to 110 maybe, but everyone I tell that keeps saying I shouldn't, because being too skinny is unhealthy.

Technically 110 puts me into the underweight category, but does that necessarily mean unhealthy?

If I just keep eating well and working out hard, how can I still be unhealthy?

I don't care so much about weight itself but the body I'm going for is kinda like this link link link (girl to the left)

They look healthy to me and I think I'd have to be at around 110 lbs to look like that. I don't want to be unhealthy though and since everyone keeps saying I would be, I'm getting kinda worried
Is weight a good indicator of bad health?
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