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Two weeks ago I joined a new company and during the hiring process I used a competing offer to increase the proposed salary.

Now that competing offer from the other company have given me almost 2x the original offer that they initially proposed. And now I want to join them for financial reasons and leave my current job during the propation period. Note that my probation period is 3 months.

How would I approach the resignation and what reason should I give, noting that my current job can easily find out that I left for the original competing company. I donot know if this will be considered unethical? This is only my second time joining a new position.

The probation period always works both ways, so it is well within your rights to make use of it and leave your current employment for greener pastures (and twice the salary is indeed greener).

Employers often like to use the "not a cultural fit" excuse to fire someone in their probation period when they don't feel like giving an yctual reason (and in order to protect themselves legally). But again, this can be used by both parties:

In your resignation tell your employer that you thank them for the opportunity, but that you don't fit into their culture.

For reasons, you can say something like

Pursuing other career prospects outside of the company which is closer to my needs.

You should not have to explain anything more.

Would it be considered unethical?

The fact that you are leaving during probation or you are quitting to go to a competitor may not be considered as unethical. However, you using offer letter from one to negotiate with another and back and forth, may be considered as unprofessional by some.

You can proceed with your choice now but I would recommend do not make it habit for every company you have offer from in future.

And now I want to join them for financial reasons and leave my current job during the probation period.

Seems you have your reasons and already made up your mind. I'd not going to say it's unethical, but somewhat unprofessional. You used the completing offer to negotiate a higher salary (to your satisfaction, I believe), and now once you have a higher remuneration offer, you don't want to continue - that somehow indicates you were not satisfied to start with and that's not a very good sign.

You can say whatever you want, but it's likely you're going to burn some bridges, more so because you mentioned

noting that my current job can easily find out that I left for the original competing company.

However, at the end of the day, a disgruntled employee is worse that no employee, so if the financial matter is highest ranking concern, you do switch. You are not compelled to put the exact details. you can provide a generic statement in the exit interview / reason for resigning as

Thanks for the opportunity, but I found another opportunity outside the organization which is better suited at this moment for me, so I chose to pursue that career path.

Suggestion for future : Next time onward, before accepting an offer, be sure to check for all possible opportunities, evaluate them and then make the final decision, at least for the remuneration part. At times, there are certain other things (work assignment, workplace culture, poor management etc.) which can lead you to make a decision to leave, but that's a different ballgame. Negotiating higher salary immediately after a negotiation and accepting the revised offer - is not going to be accepted very well.