This question is incomplete. Your information is defined not just as your belief distribution over your opponent's hands (1st order knowledge), but also your belief about his belief distribution about your hand (2nd order knowledge), and so on. The extreme case where you have perfect infinite-order knowledge is called "common knowledge", and is impossible to achieve in hold'em poker.
To take the example you gave, assume that you know your opponent's hand but he doesn't know yours. If you've been playing tight in his recall of the previous hands, you may have reason to believe that he will put you on, say, an over-pair if you go all in (in this case, AA/KK/QQ). This makes it irrational for him to call given that belief. Then this makes it rational for you to go all-in, because you will win the pot 100% of the time if you perfectly predicted his behavior. That's a case of exploiting asymmetric information (where you have better information than the opponent), which is the fundamental play of poker.
You might be interested in what optimal play looks like as information approximates common knowledge. To do that, just assume you both turn your cards up. In this case, your expected value is monotonically increasing with the amount of money you bet (which is always true in perfect information heads-up play if your odds are >0.5, regardless of whether opponent will fold or not), so you should go all in. It also turns out that he'll call (his expected value from calling is monotonically increasing with amount already in pot; in this example, the pot size is large enough relative to your maximum bet). Given 0.6*(1+1+1)<2, your expected value is actually worse off than the above case where only you had information about his hand.
In fact, take your example again, imagine if we are to change the settings and decrease the proportion of money x in the pot relative to your stack size, so that you wouldn't be worse off compared to the case in the second paragraph. Set 0.6*(x+2)=1+x, you get x=0.5. In other words, you're worse off under full information whenever x>0.5, i.e. amount of money already in pot is more than half your stacks. Let's also find the point where it no longer makes sense for him to call all-in: 0.4(x+2)=1, x=0.5, in other words he won't call all-in if x<0.5. These ranges, as you can see, have no overlap. Depending on pot size, he'll either do the same (by folding when x<0.5) or be better off (calling when x>0.5) when he has better information about your hand. This statement is in fact true generally in heads up, regardless of how you tweak the odds and cards. The fundamental theorem of poker states that better information on the part of opponents cannot hurt them (even if it's just a belief about beliefs).
The underlying reason is because heads-up poker is a two-player zero-sum game. Things are far more complicated in multi-way pots, and I won't try to expend on that here, but generally you can find cases where having better information makes you worse off.
