Why has UTXO set stopped growing since 2017-06-03?
It's hard to know for sure what's been going on. My guess would be it's a mix of :


Better coin selection algorithms used by large wallets (exchanges)
Increase in fees pushed some inefficient services to stop creating uneconomical outputs (low values). Those services would be gambling/faucets/etc.. They might now be forcing withdrawals to be above a given amount
Some services consolidating their wallets since fees have lowered a bit from the last few weeks.