If you only want hair extensions for the one day, I suggest trying a clip extension piece and bobby pinning in it in very well. They are affordable, and the least damaging on your hair. I did have the glue on extensions for about a year.
Although it did look pretty, one thing did bother me. Typically after we wash our hair, we comb our hair out, from the scalp on down. When you have extensions in, you really can not do so.
The extensions are put in right at the scalp. You can comb them gently, but to me it was irritating. I was missing that feeling of combing my hair thoroughly, scalp on down.
Now, to your question, which is less damaging. The weaving method is a bit less damaging on the hair. The glue method can leave glue stuck on our hair and a tugging method to remove it, which could cause great damage to our hair.
Another thing to keep in mind is as our hair grows, our extensions are no longer at our scalp, which makes combing more irritating. You will need to go back in to the salon and pay to have the extensions re put back in at the scalp.
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