Stats of villain:

Small sample, but villain seems to be a LAG player.
PokerStars, Hold'em No Limit - $0.02/$0.05 - 6 players
UTG: $5.00 (100 bb)
MP: $5.80 (116 bb)
CO: $10.50 (210 bb)
BU: $5.00 (100 bb)
SB (Hero): $5.46 (109 bb)
BB: $4.61 (92 bb)
Pre-Flop: ($0.07) Hero is SB with K♥ K♣
1 fold, MP raises to $0.15, 2 players fold, Hero 3-bets to $0.50, 1 fold, MP calls $0.35
Flop: ($1.05) 6♥ 4♦ T♣ (2 players)
Hero bets $0.75, MP calls $0.75
My line is standard so far.
Turn: ($2.55) A♦ (2 players)
Hero bets $0.90, MP raises to $1.80, Hero calls $0.90
I thought If is not cbet here, he would bet his Ax hand and maybe bluff with many others. Not sure about my sizing tho. Also not sure, what a minraise means here from a LAG player?
River: ($6.15) 4♥ (2 players)
Hero checks, MP bets $2.75 (all-in), Hero ???
Questions:
If I decide to cbet OTT, what sizing should I choose?
Should I fold after a minraise?
Should let him bluff and choose check/call OTT?
OTR are there any hands in his range I could beat or I completely drawing dead?