no dear, the 555 timer when configured in astable mode that is FLASHER for newbie, the R1 is used for on-time whereas R2 is used for off-time, and if you change the value of R2 that will also result in change of on-time value,
means to say
R1= change of on-time
R2= change of on-time + off-time
and 555 timer is capable of 200mAmp on its output so if you change relay from that SPDT to bigger one (although which is not required because that SPDT relay is capable of handling 5-8 Amp on 12volts whereas your starter solenoid load iss 2 amps that means SPDT is more then enough for self solenoid) the bigger relay coil put forwards more load on 555 IC and 555 IC will leak or go bad.
so transistor will be used on 555 output to drive the relay, transistors can handle heavy load.
and to avoid complications and for cost-cutting purpose we will fix the value of R2, and will use variable resistance and R1 for on-timer only.in the end your output is capable of heavy load, your off-time is fixed and on-time is adjustable.