I’ve been in the bridge business for 36 years and have no clue. It makes no sense for it to be a drain for the bridge deck, it’s too high. It makes no sense for it to be a pressure relief hole to let floodwaters from the river below pass through the bridge and not build up pressure against it- one small hole wouldn’t be suited for that. It might possibly be an access hole for utility conduits that might pass through the railing. Other than that, I got nothing.
All lame jokes aside, I don’t think these are either for lights or drainage. Given that they sit right on the expansion joints, I think they are a masonry equivalent of crush zones. Should anything make the bridge shift very much on the joints (excessive load, heavy snow, extreme temp changes, or even a minor earthquake) the side walls will break apart at these defined points. Easy to repair and limits damage to a small section of what otherwise could be tens or hundreds of feet of damaged masonry.
If it was a scupper , it would be at surface level, not a foot above.
There is one on either side of this expansion joint, but not at the other joint. It is directly over the creek, where as the other joint is not. I wondered if it might be maintenance access for a sensor, but it doesn’t make much sense for there to be one on either side, or necessary with such a low wall.
My eyes hurt from rolling after reading the bureaucratic foolishness outrage fantasy porn up thread.
That would explain why they are next to the joint, why a brick wall has survived on a steel bridge, and why the one has been recently repaired.
I was hoping for cannons…
Edit:
Except the expansion joint continues through the wall already… Still hope for cannons.
Gun ports, obviously.
The hole is not there by design, they simply ran out of bricks. 
Maybe the architect just liked the way it looked.
Is this the same bridge?
http://freepages.genealogy.rootsweb.ancestry.com/~batsto/Towns/Crosswicks/Bridge.html
If so, maybe decorative gunports is not a bad guess. Says something about Hessians using the original one before the Battle of Trenton.
Always worth keeping on the table when discussing architectural and civil design questions. 
But I’d be more inclined to think that if they were regularly spaced or, I don’t know, looked more “design intentional.” These look functional to me.
I see two other places such as you describe (one at each end). They both look to me like the metal informational plaques you often see on such bridges. I’ve seen lots of these that say something like the name of the stream, the river it drains into, what that river drains into, unique or interesting wildlife, and of course descriptions of historical events, persons, or whatever related to the building of the bridge, or who it’s named after, etc. The bronze-y looking one especially looks like that sort of plaque. The lighter-colored one also looks like something like that to me; they both appear to have (illegible, of course) text, but I have no idea why it would be different, why there would be two, or whatever. They appear to be slightly differently shaped (the one on the south end being shorter and wider than the more square-looking one on the north end).
As for the holes originally asked about, no idea. Maybe not a toll gate, but maybe a support or holder for a barrier bar in case the bridge needed to be closed or blocked due to flooding or something on one side or the other? Around here they close bridges all the time due to high water, or due to the road being washed out on the other side of the bridge, etc.
Perhaps it a covered bridge at some point, and the holes held beams.
This was my thoughts as well, but I agree it does seem to small and too few.
Looking at the holes, there’s a concrete interior, with the bricks just added as facing, and possibly not even structural. Perhaps there’s some reason the holes were there during construction, and they are no longer needed. The bricks were just added to match up with the existing hole because no one told the bricklayer otherwise.
For example, maybe the hole-less side was placed first, supported from below, but the side with the holes had to be set in place by a crane, suspended by the holes.
Could they be holes for the hooks used in moving and installing the bridge? I originally dismissed this, but if the walls are solid concrete and not masonry, then perhaps.
It could be for the fire department do drop a hose down into the river and fill up. Having it in a hole in the wall instead of on top of the wall would help keep the hose from flopping around.
Could they be required storm drains, and the contractor miscalculated the height?
It does seem that it’s a concrete bridge with a brick façade, based on looking at a close-up of the hole. That seems to be excessively labour-intensive and expensive compared to bare concrete, but then it was a public works contract in New Jersey.
Maybe the holes are to install the barricades to close a lane as needed, then?
Since the OP apparently lives near this and drives by it I’d ask that he stop his car and tell us what it says under the DP letters. Distribution Point? Disaster Prep? Down Pipe? Delivery Point? Dead People?
I’m thinking now it was a crane hookup point for when they installed that section. Or a guardrail connection point like is on the end of the bridge near the other joint.
On a whim, I googled “defence point” bridge wall - one of the top few results was this page:
Wrong country, etc, and no idea if the river under the bridge could ever be considered strategically important, but I wonder if these could be defensive features.
Is it brick on the outside, or is that just to pretty up in on-road view and add to the bucolic charm of the structure?
While he’s leaning over the railing, if it’s bare, are there other holes in the concrete structure that the workers instead bricked over on the inside?