Your furnace is shutting down on limit. There can be a number of causes for this.
Start by making sure you have a clean filter in the furnace. A dirty or restrictive filter can cause this issue. Alternatively you could also have a dirty or plugged up A/C evaporator coil which is located above your furnace. This can also cause a furnace to cycle off on high limit, however is uncommon unless you have run your furnace without a filter for prolonged periods of time. Also if you have a high efficiency furnace, there is more of a chance to have the secondary heat exchanger plug up rather than the A/C coil.
You can also have a blower motor issue. The motor can be faulty or seizing up causing it to not spin fast enough to move enough air through the furnace. Another cause may be that you have a faulty limit that is opening prematurely.
The major issue that can cause this problem is a heat exchanger issue. If your furnace is cycling off on high limit, and everything checks out, you may have an internal blockage of the heat exchanger. If this is the case either the heat exchanger or the furnace will need to be replaced. A combustion analysis of the furnace is required to prove this is the issue.
If you happen to have a 2 stage high efficiency furnace you could have a bad ventor motor gasket which is allowing air to be drawn in behind the motor. Big cracks in the condensate collector pan can also cause this but is very uncommon. You can also have the a two stage gas valve high fire solenoid stuck open, but this is also very uncommon and can only happen on 2 stage furnaces. Also if you have a bryant, payne, or carrier high efficiency, you could have a cold spot baffle leakage that is allowing air to be drawn in between the primary and secondary heat exchanger however this is also very uncommon.
If you think your blower is not spinning fast enough you may also have a bad blower motor, or if an ecm motor, the control board may be bad. If its a fixed speed motor and your getting power to it but its not spinning fast enough it could possibly be a bad blower motor. If you decide to change out the blower motor, make sure to get the appropriate replacement capacitor to go with it. I actually did have the same issue on an older carrier high efficiency furnace a few weeks back. It ended up being a bad blower motor, however the motor spun freely and had no indications of seizing or hard starting.
When you asked to increase the blower, what you are really asking to do is increase the fan speed (amount of air), right? You could ask the the tech to check/verify that you are getting 1600 CFM (cubic feet per minute) and if you truly are, and if that's not enough, ask them if it is possible to increase it (it might be adjustable). But I am thinking that may not really be the issue.
Your real problem is that it's not cooling the house. I'm not sure if this issue is truly the result of a weak blower (insufficient CFM); it's very possible, but honestly, a 1.5 ton unit is pretty small. For a 1,000 square foot house, I might recommend at least one 3 ton unit or preferentially, two 2 ton units, depending on your lattitude (summer temperature). Below is a map and chart. I would generally recommend double the what they recommend on the chart below, because you will only use what you need.
In case you didn't know, having more (AC tonnage) doesn't mean that you will use more. If you set the thermostat to say 70 °F, then the AC will turn off when the house is at 70 °F. If you have fifteen 3 ton units, you will use the same amount of energy to cool the house to 70 °F as one 2 ton unit (give or take maybe 5% energy).
![enter image description here](https://i.stack.imgur.com/rtHt5.jpg)
Map source:http://www.acdirect.com/ac-package-unit-learning-center-ac-sizing-calculator
Edit based on comment that the AC is actually a dehumidifier:
Dehumidifier? Well, that's a key piece of information. The old unit may not have been well designed as a dehumidifier; if the newer unit has been set up to be more like an actual dehumidifier then that would explain the question. The older unit was probably designed (more) for cooling. The newer unit might be a more for dehumidifying.
The difference between an air conditioner and a dehumidifier is that the air in a dehumidifier first passes through the cooling coil and then back through the heating coil (basically, there will be little change in room temp) and then back into the room as dry air. In fact, the temperature might be higher.
Unfortunately, this means that the answer is to install an actual air conditioner or re-engineer the dehumidifier to make it an air conditioner.
Edit2 Okay it's not a dehumidifier. It's a regular AC and you have a separate dehumidifier. Regular AC units have protective coatings to help prevent condensation on the evaporating/cooling coil. That protective coating usually doesn't last forever which is why older AC units often collect water. Typically, you don't want the AC to collect water (that causes rust and mold issues). For a regular AC unit, having the blower on high is okay. Lower speeds (lower CFM) may cause condensation to occur (depending on all the bells and whistles).
The dehumidifier is where you do want condensation- to remove moisture. Cooling the air should help your dehumidifier to operate, because as the temperature is lowered, the relative humidity will increase. When measuring the relative humidity, the temperature is a/the factor. For example, say that you have 44% humidity at 70 °F; it has about 0.26 grams of water/vapor per cubic foot. At 50 °F the relative humidity of 0.26 grams of vapor per cubic foot would be about 92%. A dehumidifier should be able to operate more efficiently at 92% RH than 44% RH... so that's why an AC unit can help a dehumidifier.
I suspect that when you measured the RH in the basement it was higher than you expected (maybe about the same as the RH outside), but if the temperature was lower in the basement (than outside), then having the same RH means that you actually have less water vapor in the basement, where it's cooler.
To recap: The service technician might be able to increase (or decrease) the blower speed, but that would probably lower the AC's cooling efficiency. Your new AC unit is not collecting water (yet) because the anticondensation coating hasn't been compromised (yet); and that's a good thing. A 1.5 ton AC unit may not be large enough to cool the basement. Cooling the basement should help the dehumidifier. And remember, the relative humidity is based on the temperature.
Best Answer
When I was still doing residential work the normal temperature drop across the Coil was between 15F. and 20F. A temp difference above 20F meant that more air flow was needed and a temp below 15F meant that there was too much air. Unless things have changed recently or you have a special A/C system you can use these temp drops as a guide line. Just buy a temperature thermometer or a probe type and measure the air temp difference across the coil. my 2 cents