Could a weekly payment-based contract become void if the party owed money allows the money ower to be late on payments?

Very unlikely.  If the party owed money continually allows the other party to pay late, the first party may waive the right to receive payments exactly on time, but that would not void the entire contract.  Moreover, many contracts contain clauses that provide that consenting to a modification in a given instance (like accepting a late payment) does not constitute a waiver of any contractual rights.