The following are the cases in the first 90 elements where consecutive elements do not have increasing atomic weights:

1. Tellurium (Te, atomic number 52) and Iodine (I, atomic number 53). The atomic weight of Te is 127.60, while the atomic weight of I is 126.90.

2. Cobalt (Co, atomic number 27) and Nickel (Ni, atomic number 28). The atomic weight of Co is 58.93, while the atomic weight of Ni is 58.69.

These are the only two instances among the first 90 elements where the atomic weights of consecutive elements are not in increasing order.