First off, set over set sucks, but ignoring results, I think there are some betting issues here. First, the preflop min-3 bet is too small, and you will never get any hands that min-raise to fold. That's bad for two reasons, (1) you won't fold out hands like JTs or even 98s, hands that you are flipping against, so you won't really have a clear strategy for attacking any board with overcards since you don't have a defined Villian range. (2) How will you stack someone when you flop a 7 if you are keeping the pot limited to 8BBs and a SPR of 12.5? You are hoping that your opponent is super-loose and will call off with weaker, but you will never know if they made a weaker hand on a flop like Q97 or A73.
Flop: Like Preflop, this bet seems ineffective. What are you wanting to accomplish? Extract value from overcards who will probably call a bigger bet? Bluff out a stronger hand (none will fold). Also, consider that if this flop connected to your opponent, you are now behind. A larger preflop raise would help you narrow down that it didn't help them, except for a full house or quads (random 8X and 5X hands get out to the larger raise), but as played, I don't see a way to get value on this flop, so I would bet (pot) to end the hand now. If I get called, I intend to check down to showdown if I don't improve to a full house. If I get check-raised, I will probably call once, and fold to turn aggression, noting that I'm only beating the made hands of 66, 44-22 and would have to consider objectively if my opponent would check raise and lead the turn with any of these hands or AK. Also, against a check-raise, I'm checking to showdown.
Turn: Jackpot!!! Villian's check doesn't tell me much, so now, knowing I have a nuttish hand with the full house on the PERFECT card (completes flush and straight draws), I'm betting big here. At least 2/3 pot or more ($0.60-$0.70), hoping he makes some calling mistakes with a single spade, something like As8x. He'll raise (based on action, min-raise to about $1.30). This would produce a pot of $2.86 and you have $6.98 behind. His raise indicates he has something and he is not going away. Many players consider a turn raise to be a pot-committing action and do it with strong hands. Since you also have a strong hand, you are now looking to get stacks in. In this scenario, he only has $3.43 behind, so a raise to $5 (2.8x Raise) does the trick. Because that card was so perfect, you can expect a lot of calls, including straights, flushes, trips with a random 5, overplayed overpair hands, and bluff-catching 8s. Occasionally, you will see 88, 6s4s, 6s9s and 55 (only 6 combos), but that's not a problem considering the number of times you see straights, flushes, trips, 85, and 87, so this is a highly profitable spot you want to take every time. But, as I mentioned, don't drag out the process. Each time your opponent has a decision to make on a given street, they remove more combos and make less mistakes. For example, with five rounds of betting, a competent opponent can get rid of the two pair hands, overpairs, trips, and possibly straights because that many re-raises indicate a nut-type hand, like the nut flush. Each small raise eliminates more hands you can beat and reduces the EV of the spot. Don't give your opponents so many chances to make the right play, it only costs you money in the long run.
River: All the money's in. The river brings a 9, which only improves 99 (3 more combos) to beat you. So all in all, you lose to 9 total combos (0.6% of all starting hands) and beat everything else. It's showdown time and he just so has one of the nine combos. It sucks and it happens. If it didn't, we wouldn't have a game to play.
In summary, there is probably nothing you could do to get rid of 88 in 5NL. If you want to look at it objectively, 88 won a pot it was supposed to win against 77, since you are a 4:1 dog preflop anyway. It sucks that the board gave you the strongest second-best hand possible, but getting it all-in based on this board is definitely the right way to go.
The main way to play it better is to be more aggressive with your raise sizing and not giving your opponent so many opportunities to fold to your strong hand on the turn.
Also, be honest with yourself concerning your bets and your posts to the forum. Honest assessment will make you a better poker player, and the community cannot help you become better until you are completely honest with yourself. You were not misclicking those raises. Those are intentional min-raises, which means you were not thinking about bet sizes and were just trying to drag your opponent along. At higher levels this is a mistake, because each time you min-raise, you offer greater and greater odds
on a call. Think about how you would have felt in this situation if you had A5, took this line, and your opponent called your $1.50 min-raise with 76, getting 8:1 on that call and then hitting the nine on the river. It's also highly exploitable, as someone can easily figure out that min-raises mean big hands and fold to them, so be very careful with this line and remember that it is rarely correct to min-raise for 3-bets and higher in cash games on late streets.