My Biggest Leak-River Checking

[C-Dog]

I am pretty sure that my biggest leak is checking the river when I am being called down, and there are overcards to my hand, or straight/flushes there. I should basically keep betting unless someone raises me right? Also, on most rivers where I have been betting middle pair the whole way, are the rivers usually going to be bet/fold situations? Example hand:

STAGE #169659609: HOLDEM NORMAL $1/$2 [ 2005-08-13 00:20:52 ]
Seat 6 - CHKMAN57 $72.58 in chips
Seat 7 - BART COOPER3 $17.75 in chips
Seat 9 - C_DOGGGG $60.75 in chips
Seat 1 - TEDDY41 $91 in chips
Seat 4 - ELAK $4.13 in chips
Seat 5 - EDER $40.29 in chips
*** BLIND [dealer 6] ***
BART COOPER3 - Post small blind $0.50
C_DOGGGG - Post big blind $1
C_DOGGGG - Pocket [10c,10h]
TEDDY41 - Calls $1
ELAK - Folds
EDER - Raises $1 to $2
CHKMAN57 - Folds
BART COOPER3 - Folds
C_DOGGGG - Raises $1 to $3
TEDDY41 - Calls $2
EDER - Calls $1
*** FLOP [8d,3h,2s] ***
C_DOGGGG - Bets $1
TEDDY41 - Calls $1
EDER - Raises $1 to $2
C_DOGGGG - Raises $1 to $3
TEDDY41 - Folds
EDER - Calls $1
*** TURN [8d,3h,2s,Ac] ***
C_DOGGGG - Bets $2
EDER - Calls $2
*** RIVER [8d,3h,2s,Ac,9c] ***
C_DOGGGG - Checks
EDER - Checks