Can jet fighters be made to be 2 or 3 times bigger than they are today?
The question is not whether you can do it but why would you want to.

Fighters, like any other aircraft are designed around mission profiles;  what do you want this aircraft to do, at what speeds, ranges, altitudes, combat radii, endurance, weapon carriage and employment, stealth, etc.  Therefore you would need some sort of justification for building a fighter aircraft this size.  That justification has to be so appealing that it can overcome the negative aspects of building a big fighter.  

While these profiles vary considerably between individual aircraft, they are constantly curtailed by the brutal and impartial realities of war.  Gen Stevens pointed out 4 fundamental requirements of a fighter in one of his critiques of the F-35.  These are important to remember as they have been integral in every successful fighter design over the past century of air combat.  Unfortunately, the larger the fighter, the more diametrically opposed to these realities they are and the greater the probability of failure in combat.


ATTACK YOUR ENEMY IN OVERWHELMING NUMBERS

This one is fairly simple to understand.  The greater your force is, the more difficult it is for the enemy to destroy you.  But defense ministries have limited budgets and can only spend so much on new fighters.  So the choice becomes should I buy a few advanced and highly capable fighters or lots of cheap, single purpose aircraft.  Air warfare has favored the latter.  Not only are smaller aircraft cheaper to procure, they are cheaper to operate as they burn less fuel and require less maintenance.  Consequently.  Your nation's pilot pool can get a lot of flight time in them and can become highly proficient in their operation.
SPOT YOUR ENEMY BEFORE HE SPOTS YOU

Which is going to be easier to spot from a distance: a 747 or an F-5?  Which is more likely to have a lower radar or IR signature if both employ LO features?
OUTMANEUVER AND OVERWHELM HIM

By the energy maneuvering equation, fighter design had always favored the following features:


High thrust to weight ratio
Low wing loading
Low specific fuel ratio


And this tends to favor a fighter which is basically a small, fast, nimble gas can with a compact but powerful engine and an effective armament for engaging and killing other fighters.  Not easily achievable with a larger aircraft.
KILL HIM QUICK AND MOVE ON

So now, a large, expensive, easy to spot aircraft manned by low time flight crews is now forced to engage a swarm of nimble, fast turning fighters.  They can quickly turn inside him and get to an optimal firing solution faster and more reliably.  They are also more difficult to engage and shoot using BVR weapons.  Finally OpFor has more experienced and current pilots than the larger fighter.  This now gives the larger, more expensive aircraft a very limited probability of survival.


For those reasons, history does not favor a large fighter unless it is equipped with some kind of mission system giving it a tactical advantage - and even then that is a large obstacle to overcome in terms of cost, strength, and weight.