Here's the summon spell determination (Asura, Bahamut, other) subroutine:
$03/E03B C9 3E CMP #$3E A:0000 X:0000 Y:0000 ;Compare active spell with 3E (Asura)
$03/E03D 90 1A BCC $1A [$E059] A:0000 X:0000 Y:0000 ;If less, jump down to 03/E059
$03/E03F C9 3F CMP #$3F A:0000 X:0000 Y:0000 ;If 3E or higher, compare active spell to 3F (Bahamut)
$03/E041 D0 04 BNE $04 [$E047] A:0000 X:0000 Y:0000 ;If not 3F (and therefore Asura, jump down to 03/E047
$03/E043 A9 5D LDA #$5D A:0000 X:0000 Y:0000 ;If 3f (Bahamut), load 5D into memory
$03/E045 80 18 BRA $18 [$E05F] A:0000 X:0000 Y:0000 ;Then jump down to 03/E05F (basically, end of routine)
$03/E047 A2 00 00 LDX #$0000 A:0000 X:0000 Y:0000 [this is where we jump to if Asura]
$03/E04A A9 02 LDA #$02 A:0000 X:0000 Y:0000
$03/E04C 20 79 83 JSR $8379 [$03:8379] A:0000 X:0000 Y:0000 ;Generate a random number between 00 and 02
$03/E04F 48 PHA A:0000 X:0000 Y:0000
$03/E050 A9 F8 LDA #$F8 A:0000 X:0000 Y:0000
$03/E052 8D D4 26 STA $26D4 [$7E:26D4] A:0000 X:0000 Y:0000 ;(Don't know what's going on here, seems irrelevant)
$03/E055 68 PLA A:0000 X:0000 Y:0000 ;Look at random number
$03/E056 18 CLC A:0000 X:0000 Y:0000
$03/E057 69 3E ADC #$3E A:0000 X:0000 Y:0000 ;Add 3E to random number (resulting in 3E-40)
$03/E059 38 SEC A:0000 X:0000 Y:0000 [this is where we jump to if not Asura or Bahamut]
$03/E05A E9 31 SBC #$31 A:0000 X:0000 Y:0000 ;Subtract 31 (resulting in D-F)
$03/E05C 18 CLC A:0000 X:0000 Y:0000
$03/E05D 69 4D ADC #$4D A:0000 X:0000 Y:0000 ;Add 4D (resulting in 5A-5C)
$03/E05F 8D D2 26 STA $26D2 [$7E:26D2] A:0000 X:0000 Y:0000 ;Make result new active spell
$03/E062 EE 84 35 INC $3584 [$7E:3584] A:0000 X:0000 Y:0000
$03/E065 60 RTS A:0000 X:0000 Y:0000
It would seem that there is an even chance of getting each Asura, assuming the game does an adequate job of picking a random number between 00 and 02.
In my trials, I seemed to be getting mostly 00s, less 02s, and only one or two 01s, but I didn't try enough to confidently admit weighting.
I tried looking at the ops involved in the random number selection. Sort of followed it for about 20 ops (though didn't really grasp what was going on), then just clicked through the next 100 or so ops, marveling at the crazy crap that was happening, before finally giving up.
So I am going to just run under the assumption that there is no way to affect the Asura probability.