Why bet flop here with second pair?

BB will call or raise with straight draws, flush draws, worse T's, etc etc...

This flop favors your range over that of the PF caller. You have more AA, KK, AK, KQ and other Kx hands than caller does. Also not only do you get called by draws and worse tens, you deny equity to hands like Ax and smaller pocket pairs that likely cannot continue.

The river is the street where we only bet when allied by worse or when better hands will fold. There are other considerations in play for flop and turn bets (most notably equity denial, range advantage and nut advantage).

Reasons to bet fall mostly into three categories:

1. Get worse to call
2. Get better to fold
3. Deny equity

A lot of the time many hands on the flop will bet for more than one reason. In this instance, you get worse to call and you can also deny equity from some hands. Your statement that you don't think you are getting called by better in addition to the very poorly written hand history suggests a lack of understanding. Some additional information would be useful such as:

1. What is hero's position?
2. How many people are at the table?
3. What are the effective stack sizes?
4. What solver are you looking at?
5. What are the allowed sizings in the solve you're looking at?

When betting here on the flop many worse hands call such as all straight draws and flush draws and depending on the positions and flop sizing chosen, then all worse TX, 6X, 77, 88, 99, and possibly even under pairs.

None.

But that's only one of three reasons to ever considering betting.
The other two are:

• 1. for value: You can charge the draws and worse pairs in your opponents range to continue.
  
• 2. to deny equity: If you can get villain to fold his Qx and Jx hands then you win 100% of the pot even though your hand only has 80% equity vs those hands.
  

I think something you’re missing or maybe don’t understand, you aren’t just betting a ten here, you’re betting your ‘range’ that board hits your range better than villains which gives you reason to bet, then from an exploitative view you get value from all draws, weaker tens and maybe even some smaller pocket pairs that will fish a set ott. Checking also caps your holding as this wet board isn’t one on which you’d slowplay your decent made hands on so if villain is half decent they can bet you off your hand and take the pot with bluffs by betting the turn and bombing the river (runout dependant of course)

Betting protects vs all his random overcards and draws that you don’t want seeing turns for free

Is that because his check/calling range is wider on bb than your open raise range 3bigs from the btn?

Its not wider (btns range is actually wider, depending on the sizing), but it is weaker and is capped (doesnt have the best hands). IP has both the very best hands (strong top pair+), more good hands (weak top pairs, smaller pockets like TT-QQ, good draws) and fewer hands that are absolute garbage here (low suited gappers for example). All this gives IP a sizable range advantage which allows us to bet more - we have more hands that have enough equity to be value, our bluffs/denial get more fold equity, and even with mediocre hands like second pair we dont mind folding out worse, since villain is not gonna bluff (and bet in general) as often. Well, as far as i understand it.