I use two network for weekly payout. both have a minimum of $35 a week.
clickcash and moneytree Click cash will payout the MONDAY after the week end on saturday they dont have any lagtime. while money tree mail checks on Thursday. Both pays on time, clickcash pay more per lead while mtree converts a little better for me.
Must admit though, most affiliate programs online pay monthly. Although saying that, some of the monthly paying programs may pay weekly if you can generate alot of sales.