The House of Representatives overwhelmingly approved a measure Wednesday that effectively promises $110 million to $120 million in new annual aid to cities and towns — but doesn’t officially fund the initiative just yet. Legislatures and governors have struggled to maintain their commitment to PILOT over the past two decades as surging pension and other debt costs have consumed more and more of the state budget. The second additional concept wrapped into the municipal grant bill would end the controversial practice of placing liens on the homes of former welfare recipients. The House did tackle a second, separate fiscal bill Wednesday, voting 133-13 to approve legislation that would waive state sales tax obligations for 20 years for any data center that invests at least $200 million in the state — or just $50 million if the facility is located within a state-designated enterprise zone. One potential builder, GOTSPACE Data, already has a signed project labor agreement with the building trades in eastern Connecticut.