What of the following two sentences using the phrase "beholden to" is more correct or sounds more like natural English?
I am beholding to you a lot for your helps to me.
I am being beholden to you for your help to me.
What of the following two sentences using the phrase "beholden to" is more correct or sounds more like natural English?
I am beholding to you a lot for your helps to me.
I am being beholden to you for your help to me.
The correct form is:
I am beholden to you for your help to me.
The verb behold means see. From Merriam-Webster:
transitive verb
1 : to perceive through sight or apprehension : see
2 : to gaze upon : observe. It was a pleasure to behold the beauty of the sunset. The enormous crowd was a sight to behold.intransitive verb
— used in the imperative especially to call attention.
So your first sentence, I am beholding to you, means I am observing to you, which is ungrammatical.
The adjective beholden, on the other hand, means obligated, indebted, grateful. Merriam-Webster again:
: being under obligation for a favor or gift : indebted. I'm beholden to you.
Since it is an adjective, I am being beholden is not standard English; it would be like saying I am being hungry, which we don't typically say.
Further, help is uncountable, so there is no plural form helps. Your help to me is correct, not helps.
Finally, you ask which sounds more natural. Beholden sounds very formal and archaic, to the point of stiffness. It would sound more natural to say I am grateful for your help, or more formally, I'm indebted to you for your help to me.
Neither is correct. What you're looking for is:
I am beholden to you for your help to me.
"Beholden" is not a verb, so you shouldn't conjugate it as though it were. The verb here is "to be".
Also, for what it's worth, "beholden" seems to me to be very formal. Something less formal like "Thank you for your help, I owe you one" is used more often in everyday speech.