towing travel trailer with full holding tanks?

There are several Aps for smart phones. Here is one I found.
RVDUMPS
There are many others. I call ahead before I go out of my way to make sure they will allow me to use their dump facilities.

I see you are in Arizona. I have found free sites are rare in Arizona. Some of the large RV dealers such as in Phoenix allow free dumping.

I always dump ASAP. If you look at the black tank and how it is attached to the trailer I think you will agree to dump ASAP.

Properly designed, an RV should be able to travel without issue with tanks full, unfortunately that is not always the case. As for us, we often travel with our tanks filled to some degree since we do dump our tanks at home occasionally. At least in our case, we don't notice much difference in mpg or towing characteristics whether tanks are full or empty.

However, While you are just moving it around. On many TTs. You are moving it from over the axles to the very rear of the TT, and that CAN seriously change the way the TT towes, and not for the better.

If you've been boon docking, you have basically just moved the water and the weight from the fresh water tank to the waste tanks for a net change of zero. Unless, of course, you've gotten buckets full from the creek with which to flush the commode . . . .

And yes, they are designed to carry all the tanks full, although as @bdpreece mentioned, if you go up or down very steep grades, it is possible to see some "unwanted" spillage. But that would take a pretty steep hill.

Commercial as well as state and national park campgrounds will usually let you dump in their dump stations, although they often do charge a small fee. Worst I've ever seen was $10, usually around here it is $5 or so. There are also free or nearly free dump stations at some rest areas in some states, as well as at some truck stops. I've seen them at Flying J's and Pilot stations, for example, as well as a few Walmarts, RV dealers, and camping stores.

I personally prefer to dump before leaving if the campground has a dump station simply because every pound you drag around costs fuel.

All trailers should be able to travel with full black and gray water tanks, but some can't. There are some Airstreams that have had frame issues from folks traveling with full tanks. As crazy as that sounds, some trailers just aren't built right.
Having said that, I would dump my tanks at the first reasonable opportunity.

Moved from Forum Technical Support

I OFTEN wind up traveling with at least SOME of my waste tanks full and sometimes MOST of them full but when the waste tanks are full the FW tank is empty so not that MUCH of an increase in weight. There SHOULD be no issues with towing with full tanks but some smaller trailers design the tanks as ballast so if yours is one of those you COULD notice a difference in handling. Most larger trailers (15 feet and up) don't have this issue.
Good luck / Skip

You should be able to tow easily with holding tanks full or nearly full. Actually, the travel motion will facilitate the breaking up of any solids and make the next dump much more efficient. Most campgrounds will allow passing through RVers the use of the dump station for a fee. Many truck stops (Old Flying J's) have a dump station, most charge a small fee. Some road side parks have a dump station but those are rare. Some RV dealers have a dump station also. There are apps for your smartphone that shows dump locations.

My general rule is to dump as soon as I can. We had one incident a few years ago where we camped at a lake high in the mountains with no dump sites. Although not totally full, when coming off the mountain we were at an angle where the grey tank backed up into the shower and overflowed onto the floor. As far as dumping, most rv parks will let you dump for a fee. In Oregon many state parks will let you dump for free. Some states still have free dump sites at road side rest areas.