The sum of weights is the estimate of the populatoin size. So in 1995, we had an estimated 99M households, in 2001, we had an estimated 108M households, and in 2009, 117M households. The country populatoin is growing… so I am not sure what else to expect of that sum of weights other than that it would be going up.
Multiple year weights are tricky, let’s just say that. See discussions elsewhere on this forum (what weights to use if I merge multiple years of ACS data?), as well as on ACS Data Users Community (https://acsdatacommunity.prb.org/sear…) – where you can find a couple of useful webinars.