Let F be a family of pairs of sets. We call F a (k,l)-set system if for (A,B)∈F we have that |A|=k, |B|=l, A∩B=∅. Furthermore, F is weakly intersecting if for any (Ai,Bi),(Aj,Bj)∈F with i≠j we have that Ai∩Bj and Aj∩Bi are not both empty. We give bounds on the maximum possible size of weakly intersecting (k,l)-set systems. This is joint work with Zoltán Király, Zoltán L. Nagy, and Dömötör Pálvölgyi.