Adjective for two entities of the same weight

Solution 1:

The word that has exactly the meaning that is sought here is equiponderous. Its advantage over the words proposed in the other answers is that it specifically means being of the same weight (which is what the OP asked for), rather than just being similar, comparable, matched in some way. Its disadvantages are, first, that it is arguably obsolete, and second that, even if one does not regarded it as obsolete, it is likely to be understood only by a small percentage of English speakers. So, if one wants to use a word that means of the same weight, one should say equiponderous, but if one wants to be certain that one will be understood by average people, one is likely to be better off using one of the other words proposed on this page, which do not have exactly that meaning, but are close enough.

Solution 2:

Balanced:

being in a state of balance : having different parts or elements properly or effectively arranged, proportioned, regulated, considered, etc.