Not being good at swimming, he didn't like it.
Could we omit the word "being" here?
Not good at swimming, he didn't like it.
Which one is grammatically correct?
Not being good at swimming, he didn't like it.
Could we omit the word "being" here?
Not good at swimming, he didn't like it.
Which one is grammatically correct?
Not (being) good at swimming, he didn't like it.
There is no problem omitting being in such phrases.
Other examples include
[Being] afraid of water, he didn't like swimming.
Not [being] good at swimming, he became a boxer.
See also 12 other example sentences (Numbers 12-23) in a similar question and answer at Azar Grammar Exchange. The first post is the question, and the second post gives the answers to each numbered sentence.
You can use the -ing form of a verb to give a reason by reducing a dependent clause, for example:
As he's not good at swimming, he didn't like it = Being not good at swimming, he didn't like it.
As commented by AlanCarmack, you can omit the present participle being in the participle phrase 'Not being good at swimming".