The run length limited de Bruijn (RLLdB) sequences have been studied recently owing to their application in communication systems. In each RLLdB sequence, all length-k substrings are distinct and each substring is a run length limited sequence, where there are at most s consecutive symbol 0’s. In previous work, the maximal length RLLdB sequence was designed only for the case s = 1.In this work, we propose to study a more generalised problem of constrained de Bruijn sequence, called weight bounded run length limited de Bruijn (WRdB) sequence. In each WRdB sequence, all length-k substrings are distinct and each length-k substring satisfies both constraints: the number of consecutive symbol 0’s is at most s, and the number of symbol 1’s is at least l. We aim to design a WRdB sequence with maximal length in all cases.Firstly, we build a constrained de Bruijn graph that represents a WRdB sequence and use some properties of the graph to show an upper bound on the maximal length of the sequence. Next, using Lyndon words, we present a construction of a WRdB sequence. Finally, we compute the length of the constructed WRdB sequence and show that it has the maximal length.