How much less was the pay than what you were making at the last job that your claim was based on?
Was this job the same sort of job and are those terms and conditions of having to work weekends typical to whatever is suitable work for you?
Refusing suitable work is becomes a conditional eligibility issue to continue collecting and you need to be very focused on what your state unemployment law and precedent decisions have decided in the past made a refusal of non-suitable work a winnable appeal.
Were your benefits only suspended pending an eligibility investigation into the issue, or has an appealable determination already been issued denying further benefits, which would likely also be followed up with an overpayment of benefits for the week the refusal occurred in going forward.
Unemployed people do not have a right to refuse any suitable work, but they do have a right to try to prove to the state at an appeal hearing why the work was unsuitable.
Therefore when you can prove unsuitability per the criteria of your state, refusing an offer may not be rightfully held subject to a disqualification of benefits going forward.