Weak arms (I`m a cyclists), please help!

Hi
I`m a very skinny person (6' feet tall, weight 146lbs, 3.5% body fat), my main (and only) concern about being so skinny are my arms. I want them to be as skinny as possible but I have TOO LITTLE strenght, I mean if I carry my bike on my arms for 5 minutes I`m wasted. Later that day I have a little pain on my arms, like I have lifted weights. Besides that, for road riding/racing isn`t very important, but for going downhill on a MTB it`s.
I have well core strenght but do you have any advice to get a little more strenght in my arms??
I was thinking of doing high reps at low weight for 1.5 months (4~3 days per week)...what do you think about it? I don`t want to take any juice for this...

Remember that I don`t want them (my arms) to be BIG, but have good strenght for mtb races where the upper body is more in demand than road racing.

Gaining weight is the less I want...

thanks a lot!
bye

BTW: My bike is not heavy