Configuring PIC16F877A PORTA as digital output port
It looks like this code, such as it is, is setting up the digital outputs correctly.  It is good that you used BANKSEL to eliminate any issue of possibly bad bank setting.  However, this code still has some serious problems:

There is not a single comment in sight.

How did this ever assemble!?  Opcodes aren't allowed in column 1.

Just using a HEX constant for a number of bit fields is irresponsible programming, such as your "MOVLW 0x07".  The code should be explaining what each individual bit field is and what you are therefore setting it to.  Something like this:


    banksel blonkcon1
    movlw   b'10010010'
            ; 1-------  enable the blonkulator module
            ; -XX-----  unused
            ; ---10---  prescaler of 7
            ; -----010  select single-shot operation
    movwf   blonkcon1




To test the pin setup by itself, disconnect the LEDs and just look at what the pins are doing with a scope.  There is a good chance your problem is with the circuit.  Show the complete circuit.