On the turn you improved to top pair with no kicker, which is a medium strong hand. Yet you say, that you wanted to represent a stronger hand, which is the same as turning your hand into a bluff. With a hand like this your main goal should be to try and get to a cheap showdown, and perhaps get a bit of value or deny some equity in the process.
With this in mind I am kind of on the fence about, if I even like the turn raise. Yes its a silly min-bet, but your hand is not all that great, so maybe its fine, if the turn essentially gets checked through as well. I can be ok with making a real bet on the turn though, but then I am definitely checking the river. As played you obviously can not call a raise.
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