Discussions about ranges never seem to take bluffing into account, but any time a player makes a bet they are on a possible range or else they are on a bluff (or steal), which by definition falls outside of the range. If a player eliminates all bluffs from his range, he/she becomes much more predictable for opponents.
At any time determining the “correct” size for a raise is at least partly a function of knowing what size raise is likely to intimidate opponents, particularly the blinds into folding. If a large stack is in the BB in these tournaments, they will tend to call with any two cards unless the raise is large enough to make them think they are up against a premium hand and stand to lose a significant number of chips. On the other hand, a small stack may shove with any two cards simply because they need to double up or become increasingly irrelevant. A middling low stack with a garbage hand like Q 5 o is more likely to fold to aggression.
One of the commonest reason for raising from UTG is that the player is next to go under the BB, and if the blinds are increasing and the stack is low, they need to win a set of blinds to be able to go through the next set of blinds without being increasingly depleted. If you can win one set of blinds per circuit, you can just about stay in the game, but you become increasingly vulnerable. If you can win two sets of blinds per circuit, you are ahead of the game and your stack will rapidly grow. If you win no sets of blinds per circuit, your stack will exponentially decline.
Hence as the large stack you are under much less pressure to play than the smaller stacks, and have much more to lose if you get into large pots involving whole stacks, as you can quickly go from being a leading stack with bully points to a middling stack.
This with the largest stack on the table UTG and looking down at a pair of tens, I would probably try to raise enough to make the BB fold, but fold to a shove from any reasonable sized stack who does not HAVE TO double up.
After all, if a mid size stack shoves or even puts in more than half their stack, the hands they are most likely to hold are AA, KK, QQ, JJ or some other combination of cards that contains at least one card–most likely two cards–higher than a T. Sure, you might win the slugfest, but can you afford to lose it?
I will occasionally bluff/steal from UTG by raising with a hand like 6 8 s. Here is the logic. I can win the hand if everyone folds. If I have a single flat caller, most likely he has two unpaired picture cards. If he is in the blinds, he must go first. If the flop does not contain any picture cards and he checks to me, I can probably take the pot with a meaty bet. If he check-calls, then what does he have? A set, two pairs, a pocket pair, a flush draw, a straight draw? If he has trips he will tend to be excited and check quickly hoping I will bet again. Then again, if the flop comes with two of a suit, he may be fearful that I have a flush draw and fold to a bet. If it goes to the river, I may have to give up on the hand. Another possibility is that I hit something on the flop, maybe top pair, two pairs, trips, etc.
If I have more than one caller with picture cards, then there is an increased possibility that they will block each other and I can take the pot if the flop come low, middling, and ragged.
Even if I have to give up the hand, such bluff/steal raises prepare the ground for when I really do have a premium hand and the whole table thinks it is just Mekon King trying to steal the blinds again.
You don’t always win with such a play, but you can win often enough for it to be profitable, and it does not put your whole stack or more than half your stack at risk, so is better than getting into shove fests with TT, because in tournaments the name of the game is grinding down your opponents with relentless aggression and occasionally backing off.
Look at the relative stack sizes on this hand. Note the largest stack and the size of the BB stack.
Now look at the relative stack sizes later in the tournament, both before and after this hand. Usually I will fold A 8o, but in this case it was good enough for purpose. Note that I felt my shove on the flop was relatively safe, because most likely one of the blinds would have led out with a Jack, and being large stacks were relatively loose callers. Also the fact that I held the Ace of Diamonds made it much less likely that either opponent had a diamond flush draw.
I know I have not totally answered your questions, but I think the points made here are somewhat relevant to the original issue.
Finally, and this is a bit off topic, I would like to present a very interesting hand that I posted elsewhere, but seem to have lost and would appreciate any comments on the play: