> as I work on Saturday-Sundays as well.
You are underselling your self and will sound needy to any recruiter.
> I want ... stable and robust job even if it means I get paid low.
Again, not good to undersell yourself.
> I am ok to work on Sat-Sun.
Don't promise this on the get go as I mentioned before.
You should focus on your network. Work on what your strengths are and what value will you bring to a company. If you keep repeating the Sat/Sun you will get a job that will burn you and you will be looking for another job within months. Just my 2cents.