We explore the maximum total number of edge crossings and the maximum geometric thickness of the Euclidean minimum-weight (k, ℓ)-tight graph on a planar point set P. In this paper, we show that (10/7－ε)|P| and (11/6－ε)|P| are lower bounds for the maximum total number of edge crossings for any ε ＞ 0 in cases (k,ℓ)=(2,3) and (2,2), respectively. We also show that the lower bound for the maximum geometric thickness is 3 for both cases. In the proofs, we apply the method of arranging isomorphic units regularly. While the method is developed for the proof in case (k,ℓ)=(2,3), it also works for different ℓ.