WIthout a reading!

Sometimes these guys will do it with AT

PokerStars No-Limit Hold'em, $0.10 BB (7 handed) from (Format: FlopTurnRiver)

UTG ($23.10)
MP1 ($3.05)
MP2 ($14.35)
CO ($9.25)
Button ($6.90)
SB ($1.70)
Hero ($10.45)

Preflop: Hero is BB with K, K.
UTG calls $0.10, 3 folds, Button raises to $0.2, 1 fold, Hero raises to $0.6, UTG calls $0.50, Button calls $0.40.

Flop: ($1.85) 7, 3, T (3 players)
Hero bets $1.8, UTG calls $1.80, Button raises to $3.6, Hero raises to $9.85, UTG folds, Button calls $2.70 (All-In).

Turn: ($19.80) J (2 players, 1 all-in)

River: ($19.80) 7 (2 players, 1 all-in)

Final Pot: $19.80

Results in white below:
Hero has Kd Kh (two pair, kings and sevens).
Button has 3d 3h (full house, threes full of sevens).
Outcome: Button wins $16.25. Hero wins $3.55.

Do I fold to that mini raise every time without a reading?

Flop: ($1.85) 7, 3, T (3 players)
Hero bets $1.8, UTG calls $1.80, Button raises to $3.6,

You bet pot and had a caller, now BTN min-raises. Something any good poker player should learn... one of the easiest tells is min-raises in these types of spots. They obviously want you to call or push back, and they are NOT folding. With less than two-pair, I'd let it go.

Very good point about the in betweem caller, I did not see it from the min raiser point of view. It was obvious he wouldnt do that with any less than one pair

A minimum raise after a call definitely wants a raise, most of the time. At $10 NL that may not always be the case, but as you move up you will want the practice of folding in this type of situation. Might as well start now, even if you let some donk bluff you out of a hand or two along the way.

Preflop raise is really bad. It need at least $1.

The min raise is a set alot of the time, but theres no way you can fold in this spot. The pot is raised and reraised preflop and hes short stacked. Just shove it in. (but raise more preflop next time)